Algebra Examples

$7 x + x^{2} = - 4$

Step 1

Add $4$ to both sides of the equation.

$7 x + x^{2} + 4 = 0$

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 $a = 1$ , $b = 7$ , and $c = 4$ into the quadratic formula and solve for $x$ .

$\frac{- 7 \pm \sqrt{7^{2} - 4 \cdot (1 \cdot 4)}}{2 \cdot 1}$

Step 4

Simplify.

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Step 4.1

Simplify the numerator.

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Step 4.1.1

Raise $7$ to the power of $2$ .

$x = \frac{- 7 \pm \sqrt{49 - 4 \cdot 1 \cdot 4}}{2 \cdot 1}$

Step 4.1.2

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

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Step 4.1.2.1

Multiply $- 4$ by $1$ .

$x = \frac{- 7 \pm \sqrt{49 - 4 \cdot 4}}{2 \cdot 1}$

Step 4.1.2.2

Multiply $- 4$ by $4$ .

$x = \frac{- 7 \pm \sqrt{49 - 16}}{2 \cdot 1}$

Step 4.1.3

Subtract $16$ from $49$ .

$x = \frac{- 7 \pm \sqrt{33}}{2 \cdot 1}$

Step 4.2

Multiply $2$ by $1$ .

$x = \frac{- 7 \pm \sqrt{33}}{2}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \frac{- 7 \pm \sqrt{33}}{2}$

Decimal Form:

$x = - 0.62771867 \dots, - 6.37228132 \dots$