Finite Math Examples

$6 x + \sqrt{y} - 7 = 0$

Step 1

Move all terms not containing $\sqrt{y}$ to the right side of the equation.

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Step 1.1

Subtract $6 x$ from both sides of the equation.

$\sqrt{y} - 7 = - 6 x$

Step 1.2

Add $7$ to both sides of the equation.

$\sqrt{y} = - 6 x + 7$

Step 2

To remove the radical on the left side of the equation, square both sides of the equation.

${\sqrt{y}}^{2} = {(- 6 x + 7)}^{2}$

Step 3

Simplify each side of the equation.

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Step 3.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{y}$ as $y^{\frac{1}{2}}$ .

${(y^{\frac{1}{2}})}^{2} = {(- 6 x + 7)}^{2}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Simplify ${(y^{\frac{1}{2}})}^{2}$ .

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Step 3.2.1.1

Multiply the exponents in ${(y^{\frac{1}{2}})}^{2}$ .

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Step 3.2.1.1.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$y^{\frac{1}{2} \cdot 2} = {(- 6 x + 7)}^{2}$

Step 3.2.1.1.2

Cancel the common factor of $2$ .

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Step 3.2.1.1.2.1

Cancel the common factor.

$y^{\frac{1}{2} \cdot 2} = {(- 6 x + 7)}^{2}$

Step 3.2.1.1.2.2

Rewrite the expression.

$y^{1} = {(- 6 x + 7)}^{2}$

Step 3.2.1.2

Simplify.

$y = {(- 6 x + 7)}^{2}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Simplify ${(- 6 x + 7)}^{2}$ .

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Step 3.3.1.1

Rewrite ${(- 6 x + 7)}^{2}$ as $(- 6 x + 7) (- 6 x + 7)$ .

$y = (- 6 x + 7) (- 6 x + 7)$

Step 3.3.1.2

Expand $(- 6 x + 7) (- 6 x + 7)$ using the FOIL Method.

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Step 3.3.1.2.1

Apply the distributive property.

$y = - 6 x (- 6 x + 7) + 7 (- 6 x + 7)$

Step 3.3.1.2.2

Apply the distributive property.

$y = - 6 x (- 6 x) - 6 x \cdot 7 + 7 (- 6 x + 7)$

Step 3.3.1.2.3

Apply the distributive property.

$y = - 6 x (- 6 x) - 6 x \cdot 7 + 7 (- 6 x) + 7 \cdot 7$

Step 3.3.1.3

Simplify and combine like terms.

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Step 3.3.1.3.1

Simplify each term.

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Step 3.3.1.3.1.1

Rewrite using the commutative property of multiplication.

$y = - 6 \cdot - 6 x \cdot x - 6 x \cdot 7 + 7 (- 6 x) + 7 \cdot 7$

Step 3.3.1.3.1.2

Multiply $x$ by $x$ by adding the exponents.

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Step 3.3.1.3.1.2.1

Move $x$ .

$y = - 6 \cdot - 6 (x \cdot x) - 6 x \cdot 7 + 7 (- 6 x) + 7 \cdot 7$

Step 3.3.1.3.1.2.2

Multiply $x$ by $x$ .

$y = - 6 \cdot - 6 x^{2} - 6 x \cdot 7 + 7 (- 6 x) + 7 \cdot 7$

Step 3.3.1.3.1.3

Multiply $- 6$ by $- 6$ .

$y = 36 x^{2} - 6 x \cdot 7 + 7 (- 6 x) + 7 \cdot 7$

Step 3.3.1.3.1.4

Multiply $7$ by $- 6$ .

$y = 36 x^{2} - 42 x + 7 (- 6 x) + 7 \cdot 7$

Step 3.3.1.3.1.5

Multiply $- 6$ by $7$ .

$y = 36 x^{2} - 42 x - 42 x + 7 \cdot 7$

Step 3.3.1.3.1.6

Multiply $7$ by $7$ .

$y = 36 x^{2} - 42 x - 42 x + 49$

Step 3.3.1.3.2

Subtract $42 x$ from $- 42 x$ .

$y = 36 x^{2} - 84 x + 49$