Algebra Examples

$- \frac{8}{5}$ , $\frac{9}{5}$

Step 1

$x = - \frac{8}{5}$ and $x = \frac{9}{5}$ are the two real distinct solutions for the quadratic equation, which means that $x + \frac{8}{5}$ and $x - \frac{9}{5}$ are the factors of the quadratic equation.

$(x + \frac{8}{5}) (x - \frac{9}{5}) = 0$

Step 2

Expand $(x + \frac{8}{5}) (x - \frac{9}{5})$ using the FOIL Method.

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Apply the distributive property.

$x (x - \frac{9}{5}) + \frac{8}{5} \cdot (x - \frac{9}{5}) = 0$

Apply the distributive property.

$x \cdot x + x (- \frac{9}{5}) + \frac{8}{5} \cdot (x - \frac{9}{5}) = 0$

Apply the distributive property.

$x \cdot x + x (- \frac{9}{5}) + \frac{8}{5} x + \frac{8}{5} \cdot (- \frac{9}{5}) = 0$

Step 3

Simplify and combine like terms.

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Simplify each term.

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Multiply $x$ by $x$ .

$x^{2} + x (- \frac{9}{5}) + \frac{8}{5} x + \frac{8}{5} \cdot (- \frac{9}{5}) = 0$

Combine $x$ and $\frac{9}{5}$ .

$x^{2} - \frac{x \cdot 9}{5} + \frac{8}{5} x + \frac{8}{5} \cdot (- \frac{9}{5}) = 0$

Move $9$ to the left of $x$ .

$x^{2} - \frac{9 \cdot x}{5} + \frac{8}{5} x + \frac{8}{5} \cdot (- \frac{9}{5}) = 0$

Combine $\frac{8}{5}$ and $x$ .

$x^{2} - \frac{9 x}{5} + \frac{8 x}{5} + \frac{8}{5} \cdot (- \frac{9}{5}) = 0$

Multiply $\frac{8}{5} (- \frac{9}{5})$ .

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Multiply $\frac{8}{5}$ by $\frac{9}{5}$ .

$x^{2} - \frac{9 x}{5} + \frac{8 x}{5} - \frac{8 \cdot 9}{5 \cdot 5} = 0$

Multiply $8$ by $9$ .

$x^{2} - \frac{9 x}{5} + \frac{8 x}{5} - \frac{72}{5 \cdot 5} = 0$

Multiply $5$ by $5$ .

$x^{2} - \frac{9 x}{5} + \frac{8 x}{5} - \frac{72}{25} = 0$

Combine the numerators over the common denominator.

$x^{2} + \frac{- 9 x + 8 x}{5} - \frac{72}{25} = 0$

Step 4

Add $- 9 x$ and $8 x$ .

$x^{2} + \frac{- x}{5} - \frac{72}{25} = 0$

Step 5

Move the negative in front of the fraction.

$x^{2} - \frac{x}{5} - \frac{72}{25} = 0$

Step 6

The standard quadratic equation using the given set of solutions ${- \frac{8}{5}, \frac{9}{5}}$ is $y = x^{2} - \frac{x}{5} - \frac{72}{25}$ .

$y = x^{2} - \frac{x}{5} - \frac{72}{25}$

Step 7