Precalculus Examples

$(7, - 8)$

Step 1

$x = 7$ and $x = - 8$ are the two real distinct solutions for the quadratic equation, which means that $x - 7$ and $x + 8$ are the factors of the quadratic equation.

$(x - 7) (x + 8) = 0$

Step 2

Expand $(x - 7) (x + 8)$ using the FOIL Method.

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Step 2.1

Apply the distributive property.

$x (x + 8) - 7 (x + 8) = 0$

Step 2.2

Apply the distributive property.

$x \cdot x + x \cdot 8 - 7 (x + 8) = 0$

Step 2.3

Apply the distributive property.

$x \cdot x + x \cdot 8 - 7 x - 7 \cdot 8 = 0$

Step 3

Simplify and combine like terms.

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Step 3.1

Simplify each term.

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Step 3.1.1

Multiply $x$ by $x$ .

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

Step 3.1.2

Move $8$ to the left of $x$ .

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

Step 3.1.3

Multiply $- 7$ by $8$ .

$x^{2} + 8 x - 7 x - 56 = 0$

Step 3.2

Subtract $7 x$ from $8 x$ .

$x^{2} + x - 56 = 0$

Step 4

The standard quadratic equation using the given set of solutions ${7, - 8}$ is $y = x^{2} + x - 56$ .

$y = x^{2} + x - 56$

Step 5