Algebra Examples

$10 x^{2} - y = 48$ $2 y = 16 x^{2} + 48$

Step 1

Divide each term in $2 y = 16 x^{2} + 48$ by $2$ and simplify.

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Step 1.1

Divide each term in $2 y = 16 x^{2} + 48$ by $2$ .

$\frac{2 y}{2} = \frac{16 x^{2}}{2} + \frac{48}{2}$

$10 x^{2} - y = 48$

Step 1.2

Simplify the left side.

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Step 1.2.1

Cancel the common factor of $2$ .

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Step 1.2.1.1

Cancel the common factor.

$\frac{2 y}{2} = \frac{16 x^{2}}{2} + \frac{48}{2}$

$10 x^{2} - y = 48$

Step 1.2.1.2

Divide $y$ by $1$ .

$y = \frac{16 x^{2}}{2} + \frac{48}{2}$

$10 x^{2} - y = 48$

$y = \frac{16 x^{2}}{2} + \frac{48}{2}$

$10 x^{2} - y = 48$

$y = \frac{16 x^{2}}{2} + \frac{48}{2}$

$10 x^{2} - y = 48$

Step 1.3

Simplify the right side.

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Step 1.3.1

Simplify each term.

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Step 1.3.1.1

Cancel the common factor of $16$ and $2$ .

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Step 1.3.1.1.1

Factor $2$ out of $16 x^{2}$ .

$y = \frac{2 (8 x^{2})}{2} + \frac{48}{2}$

$10 x^{2} - y = 48$

Step 1.3.1.1.2

Cancel the common factors.

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Step 1.3.1.1.2.1

Factor $2$ out of $2$ .

$y = \frac{2 (8 x^{2})}{2 (1)} + \frac{48}{2}$

$10 x^{2} - y = 48$

Step 1.3.1.1.2.2

Cancel the common factor.

$y = \frac{2 (8 x^{2})}{2 \cdot 1} + \frac{48}{2}$

$10 x^{2} - y = 48$

Step 1.3.1.1.2.3

Rewrite the expression.

$y = \frac{8 x^{2}}{1} + \frac{48}{2}$

$10 x^{2} - y = 48$

Step 1.3.1.1.2.4

Divide $8 x^{2}$ by $1$ .

$y = 8 x^{2} + \frac{48}{2}$

$10 x^{2} - y = 48$

$y = 8 x^{2} + \frac{48}{2}$

$10 x^{2} - y = 48$

$y = 8 x^{2} + \frac{48}{2}$

$10 x^{2} - y = 48$

Step 1.3.1.2

Divide $48$ by $2$ .

$y = 8 x^{2} + 24$

$10 x^{2} - y = 48$

$y = 8 x^{2} + 24$

$10 x^{2} - y = 48$

$y = 8 x^{2} + 24$

$10 x^{2} - y = 48$

$y = 8 x^{2} + 24$

$10 x^{2} - y = 48$

Step 2

Replace all occurrences of $y$ with $8 x^{2} + 24$ in each equation.

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Step 2.1

Replace all occurrences of $y$ in $10 x^{2} - y = 48$ with $8 x^{2} + 24$ .

$10 x^{2} - (8 x^{2} + 24) = 48$

$y = 8 x^{2} + 24$

Step 2.2

Simplify the left side.

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Step 2.2.1

Simplify $10 x^{2} - (8 x^{2} + 24)$ .

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Step 2.2.1.1

Simplify each term.

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Step 2.2.1.1.1

Apply the distributive property.

$10 x^{2} - (8 x^{2}) - 1 \cdot 24 = 48$

$y = 8 x^{2} + 24$

Step 2.2.1.1.2

Multiply $8$ by $- 1$ .

$10 x^{2} - 8 x^{2} - 1 \cdot 24 = 48$

$y = 8 x^{2} + 24$

Step 2.2.1.1.3

Multiply $- 1$ by $24$ .

$10 x^{2} - 8 x^{2} - 24 = 48$

$y = 8 x^{2} + 24$

$10 x^{2} - 8 x^{2} - 24 = 48$

$y = 8 x^{2} + 24$

Step 2.2.1.2

Subtract $8 x^{2}$ from $10 x^{2}$ .

$2 x^{2} - 24 = 48$

$y = 8 x^{2} + 24$

$2 x^{2} - 24 = 48$

$y = 8 x^{2} + 24$

$2 x^{2} - 24 = 48$

$y = 8 x^{2} + 24$

$2 x^{2} - 24 = 48$

$y = 8 x^{2} + 24$

Step 3

Solve for $x$ in $2 x^{2} - 24 = 48$ .

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Step 3.1

Move all terms not containing $x$ to the right side of the equation.

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Step 3.1.1

Add $24$ to both sides of the equation.

$2 x^{2} = 48 + 24$

$y = 8 x^{2} + 24$

Step 3.1.2

Add $48$ and $24$ .

$2 x^{2} = 72$

$y = 8 x^{2} + 24$

$2 x^{2} = 72$

$y = 8 x^{2} + 24$

Step 3.2

Divide each term in $2 x^{2} = 72$ by $2$ and simplify.

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Step 3.2.1

Divide each term in $2 x^{2} = 72$ by $2$ .

$\frac{2 x^{2}}{2} = \frac{72}{2}$

$y = 8 x^{2} + 24$

Step 3.2.2

Simplify the left side.

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Step 3.2.2.1

Cancel the common factor of $2$ .

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Step 3.2.2.1.1

Cancel the common factor.

$\frac{2 x^{2}}{2} = \frac{72}{2}$

$y = 8 x^{2} + 24$

Step 3.2.2.1.2

Divide $x^{2}$ by $1$ .

$x^{2} = \frac{72}{2}$

$y = 8 x^{2} + 24$

$x^{2} = \frac{72}{2}$

$y = 8 x^{2} + 24$

$x^{2} = \frac{72}{2}$

$y = 8 x^{2} + 24$

Step 3.2.3

Simplify the right side.

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Step 3.2.3.1

Divide $72$ by $2$ .

$x^{2} = 36$

$y = 8 x^{2} + 24$

$x^{2} = 36$

$y = 8 x^{2} + 24$

$x^{2} = 36$

$y = 8 x^{2} + 24$

Step 3.3

Take the specified root of both sides of the equation to eliminate the exponent on the left side.

$x = \pm \sqrt{36}$

$y = 8 x^{2} + 24$

Step 3.4

Simplify $\pm \sqrt{36}$ .

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Step 3.4.1

Rewrite $36$ as $6^{2}$ .

$x = \pm \sqrt{6^{2}}$

$y = 8 x^{2} + 24$

Step 3.4.2

Pull terms out from under the radical, assuming positive real numbers.

$x = \pm 6$

$y = 8 x^{2} + 24$

$x = \pm 6$

$y = 8 x^{2} + 24$

Step 3.5

The complete solution is the result of both the positive and negative portions of the solution.

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Step 3.5.1

First, use the positive value of the $\pm$ to find the first solution.

$x = 6$

$y = 8 x^{2} + 24$

Step 3.5.2

Next, use the negative value of the $\pm$ to find the second solution.

$x = - 6$

$y = 8 x^{2} + 24$

Step 3.5.3

The complete solution is the result of both the positive and negative portions of the solution.

$x = 6, - 6$

$y = 8 x^{2} + 24$

$x = 6, - 6$

$y = 8 x^{2} + 24$

$x = 6, - 6$

$y = 8 x^{2} + 24$

Step 4

Replace all occurrences of $x$ with $6$ in each equation.

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Step 4.1

Replace all occurrences of $x$ in $y = 8 x^{2} + 24$ with $6$ .

$y = 8 {(6)}^{2} + 24$

$x = 6$

Step 4.2

Simplify the right side.

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Step 4.2.1

Simplify $8 {(6)}^{2} + 24$ .

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Step 4.2.1.1

Simplify each term.

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Step 4.2.1.1.1

Raise $6$ to the power of $2$ .

$y = 8 \cdot 36 + 24$

$x = 6$

Step 4.2.1.1.2

Multiply $8$ by $36$ .

$y = 288 + 24$

$x = 6$

$y = 288 + 24$

$x = 6$

Step 4.2.1.2

Add $288$ and $24$ .

$y = 312$

$x = 6$

$y = 312$

$x = 6$

$y = 312$

$x = 6$

$y = 312$

$x = 6$

Step 5

Replace all occurrences of $x$ with $- 6$ in each equation.

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Step 5.1

Replace all occurrences of $x$ in $y = 8 x^{2} + 24$ with $- 6$ .

$y = 8 {(- 6)}^{2} + 24$

$x = - 6$

Step 5.2

Simplify the right side.

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Step 5.2.1

Simplify $8 {(- 6)}^{2} + 24$ .

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Step 5.2.1.1

Simplify each term.

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Step 5.2.1.1.1

Raise $- 6$ to the power of $2$ .

$y = 8 \cdot 36 + 24$

$x = - 6$

Step 5.2.1.1.2

Multiply $8$ by $36$ .

$y = 288 + 24$

$x = - 6$

$y = 288 + 24$

$x = - 6$

Step 5.2.1.2

Add $288$ and $24$ .

$y = 312$

$x = - 6$

$y = 312$

$x = - 6$

$y = 312$

$x = - 6$

$y = 312$

$x = - 6$

Step 6

The solution to the system is the complete set of ordered pairs that are valid solutions.

$(6, 312)$

$(- 6, 312)$

Step 7

The result can be shown in multiple forms.

Point Form:

$(6, 312), (- 6, 312)$

Equation Form:

$x = 6, y = 312$

$x = - 6, y = 312$

Step 8