Solve Using the Quadratic Formula (x-7)(2x+5)=0

$(x - 7) (2 x + 5) = 0$

Step 1

Simplify the left side.

Simplify $(x - 7) (2 x + 5)$ .

Expand $(x - 7) (2 x + 5)$ using the FOIL Method.

Apply the distributive property.

$x (2 x + 5) - 7 (2 x + 5) = 0$

Apply the distributive property.

$x (2 x) + x \cdot 5 - 7 (2 x + 5) = 0$

Apply the distributive property.

$x (2 x) + x \cdot 5 - 7 (2 x) - 7 \cdot 5 = 0$

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$2 x \cdot x + x \cdot 5 - 7 (2 x) - 7 \cdot 5 = 0$

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

Move $x$ .

$2 (x \cdot x) + x \cdot 5 - 7 (2 x) - 7 \cdot 5 = 0$

Multiply $x$ by $x$ .

$2 x^{2} + x \cdot 5 - 7 (2 x) - 7 \cdot 5 = 0$

Move $5$ to the left of $x$ .

$2 x^{2} + 5 \cdot x - 7 (2 x) - 7 \cdot 5 = 0$

Multiply $2$ by $- 7$ .

$2 x^{2} + 5 x - 14 x - 7 \cdot 5 = 0$

Multiply $- 7$ by $5$ .

$2 x^{2} + 5 x - 14 x - 35 = 0$

Subtract $14 x$ from $5 x$ .

$2 x^{2} - 9 x - 35 = 0$

Step 2

Use the quadratic formula to find the solutions.

$\frac{- b \pm \sqrt{b^{2} - 4 (a c)}}{2 a}$

Step 3

Substitute the values $a = 2$ , $b = - 9$ , and $c = - 35$ into the quadratic formula and solve for $x$ .

$\frac{9 \pm \sqrt{{(- 9)}^{2} - 4 \cdot (2 \cdot - 35)}}{2 \cdot 2}$

Step 4

Simplify.

Simplify the numerator.

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

$x = \frac{9 \pm \sqrt{81 - 4 \cdot 2 \cdot - 35}}{2 \cdot 2}$

Multiply $- 4 \cdot 2 \cdot - 35$ .

Multiply $- 4$ by $2$ .

$x = \frac{9 \pm \sqrt{81 - 8 \cdot - 35}}{2 \cdot 2}$

Multiply $- 8$ by $- 35$ .

$x = \frac{9 \pm \sqrt{81 + 280}}{2 \cdot 2}$

Add $81$ and $280$ .

$x = \frac{9 \pm \sqrt{361}}{2 \cdot 2}$

Rewrite $361$ as $19^{2}$ .

$x = \frac{9 \pm \sqrt{19^{2}}}{2 \cdot 2}$

Pull terms out from under the radical, assuming positive real numbers.

$x = \frac{9 \pm 19}{2 \cdot 2}$

Multiply $2$ by $2$ .

$x = \frac{9 \pm 19}{4}$

Step 5

The final answer is the combination of both solutions.

$x = 7, - \frac{5}{2}$

Solve Using the Quadratic Formula (x-7)(2x+5)=0

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