Algebra Examples

$2 x (x - 4) = x + 5$

Step 1

Move all terms to the left side of the equation and simplify.

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Step 1.1

Simplify the left side.

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Step 1.1.1

Simplify $2 x (x - 4)$ .

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Step 1.1.1.1

Apply the distributive property.

$2 x \cdot x + 2 x \cdot - 4 = x + 5$

Step 1.1.1.2

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

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Step 1.1.1.2.1

Move $x$ .

$2 (x \cdot x) + 2 x \cdot - 4 = x + 5$

Step 1.1.1.2.2

Multiply $x$ by $x$ .

$2 x^{2} + 2 x \cdot - 4 = x + 5$

Step 1.1.1.3

Multiply $- 4$ by $2$ .

$2 x^{2} - 8 x = x + 5$

Step 1.2

Move all the expressions to the left side of the equation.

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Step 1.2.1

Subtract $x$ from both sides of the equation.

$2 x^{2} - 8 x - x = 5$

Step 1.2.2

Subtract $5$ from both sides of the equation.

$2 x^{2} - 8 x - x - 5 = 0$

Step 1.3

Subtract $x$ from $- 8 x$ .

$2 x^{2} - 9 x - 5 = 0$

Step 2

The discriminant of a quadratic is the expression inside the radical of the quadratic formula.

$b^{2} - 4 (a c)$

Step 3

Substitute in the values of $a$ , $b$ , and $c$ .

${(- 9)}^{2} - 4 (2 \cdot - 5)$

Step 4

Evaluate the result to find the discriminant.

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Step 4.1

Simplify each term.

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Step 4.1.1

Raise $- 9$ to the power of $2$ .

$81 - 4 (2 \cdot - 5)$

Step 4.1.2

Multiply $- 4 (2 \cdot - 5)$ .

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Step 4.1.2.1

Multiply $2$ by $- 5$ .

$81 - 4 \cdot - 10$

Step 4.1.2.2

Multiply $- 4$ by $- 10$ .

$81 + 40$

Step 4.2

Add $81$ and $40$ .

$121$