Algebra Examples

$x^{2} + 2 x = 35$

Step 1

Subtract $35$ from both sides of the equation.

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

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 $a = 1$ , $b = 2$ , and $c = - 35$ into the quadratic formula and solve for $x$ .

$\frac{- 2 \pm \sqrt{2^{2} - 4 \cdot (1 \cdot - 35)}}{2 \cdot 1}$

Step 4

Simplify.

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Step 4.1

Simplify the numerator.

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Step 4.1.1

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

$x = \frac{- 2 \pm \sqrt{4 - 4 \cdot 1 \cdot - 35}}{2 \cdot 1}$

Step 4.1.2

Multiply $- 4 \cdot 1 \cdot - 35$ .

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Step 4.1.2.1

Multiply $- 4$ by $1$ .

$x = \frac{- 2 \pm \sqrt{4 - 4 \cdot - 35}}{2 \cdot 1}$

Step 4.1.2.2

Multiply $- 4$ by $- 35$ .

$x = \frac{- 2 \pm \sqrt{4 + 140}}{2 \cdot 1}$

Step 4.1.3

Add $4$ and $140$ .

$x = \frac{- 2 \pm \sqrt{144}}{2 \cdot 1}$

Step 4.1.4

Rewrite $144$ as $12^{2}$ .

$x = \frac{- 2 \pm \sqrt{12^{2}}}{2 \cdot 1}$

Step 4.1.5

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

$x = \frac{- 2 \pm 12}{2 \cdot 1}$

Step 4.2

Multiply $2$ by $1$ .

$x = \frac{- 2 \pm 12}{2}$

Step 4.3

Simplify $\frac{- 2 \pm 12}{2}$ .

$x = - 1 \pm 6$

Step 5

The final answer is the combination of both solutions.

$x = 5, - 7$