Algebra Examples

$2 x (x - 4) = - 13 x + 7$

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.

$2 x \cdot x + 2 x \cdot - 4 = - 13 x + 7$

Step 1.1.1.2

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

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Step 1.1.1.2.1

Move $x$ .

$2 (x \cdot x) + 2 x \cdot - 4 = - 13 x + 7$

Step 1.1.1.2.2

Multiply $x$ by $x$ .

$2 x^{2} + 2 x \cdot - 4 = - 13 x + 7$

Step 1.1.1.3

Multiply $- 4$ by $2$ .

$2 x^{2} - 8 x = - 13 x + 7$

Step 1.2

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

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Step 1.2.1

Add $13 x$ to both sides of the equation.

$2 x^{2} - 8 x + 13 x = 7$

Step 1.2.2

Subtract $7$ from both sides of the equation.

$2 x^{2} - 8 x + 13 x - 7 = 0$

Step 1.3

Add $- 8 x$ and $13 x$ .

$2 x^{2} + 5 x - 7 = 0$

Step 2

Once the quadratic is in standard form, the values of $a$ , $b$ , and $c$ can be found.

$a x^{2} + b x + c$

Step 3

Use the standard form of the equation to find $a$ , $b$ , and $c$ for this quadratic.

$a = 2$ , $b = 5$ , $c = - 7$