Algebra Examples

9 = - 7 x + 7 x^{2}

$9 = - 7 x + 7 x^{2}$

Step 1

Move all the expressions to the left side of the equation.

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Step 1.1

Add

7 x

$7 x$ to both sides of the equation.

9 + 7 x = 7 x^{2}

$9 + 7 x = 7 x^{2}$

Step 1.2

Subtract

7 x^{2}

$7 x^{2}$ from both sides of the equation.

9 + 7 x - 7 x^{2} = 0

$9 + 7 x - 7 x^{2} = 0$

9 + 7 x - 7 x^{2} = 0

$9 + 7 x - 7 x^{2} = 0$

Step 2

Use the quadratic formula to find the solutions.

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

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

Step 3

Substitute the values

a = - 7

$a = - 7$ ,

b = 7

$b = 7$ , and

c = 9

$c = 9$ into the quadratic formula and solve for

x

$x$ .

\frac{- 7 \pm \sqrt{7^{2} - 4 \cdot (- 7 \cdot 9)}}{2 \cdot - 7}

$\frac{- 7 \pm \sqrt{7^{2} - 4 \cdot (- 7 \cdot 9)}}{2 \cdot - 7}$

Step 4

Simplify.

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Step 4.1

Simplify the numerator.

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Step 4.1.1

Raise

7

$7$ to the power of

2

$2$ .

x = \frac{- 7 \pm \sqrt{49 - 4 \cdot - 7 \cdot 9}}{2 \cdot - 7}

$x = \frac{- 7 \pm \sqrt{49 - 4 \cdot - 7 \cdot 9}}{2 \cdot - 7}$

Step 4.1.2

Multiply

- 4 \cdot - 7 \cdot 9

$- 4 \cdot - 7 \cdot 9$ .

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Step 4.1.2.1

Multiply

- 4

$- 4$ by

- 7

$- 7$ .

x = \frac{- 7 \pm \sqrt{49 + 28 \cdot 9}}{2 \cdot - 7}

$x = \frac{- 7 \pm \sqrt{49 + 28 \cdot 9}}{2 \cdot - 7}$

Step 4.1.2.2

Multiply

28

$28$ by

9

$9$ .

x = \frac{- 7 \pm \sqrt{49 + 252}}{2 \cdot - 7}

$x = \frac{- 7 \pm \sqrt{49 + 252}}{2 \cdot - 7}$

x = \frac{- 7 \pm \sqrt{49 + 252}}{2 \cdot - 7}

$x = \frac{- 7 \pm \sqrt{49 + 252}}{2 \cdot - 7}$

Step 4.1.3

Add

49

$49$ and

252

$252$ .

x = \frac{- 7 \pm \sqrt{301}}{2 \cdot - 7}

$x = \frac{- 7 \pm \sqrt{301}}{2 \cdot - 7}$

x = \frac{- 7 \pm \sqrt{301}}{2 \cdot - 7}

$x = \frac{- 7 \pm \sqrt{301}}{2 \cdot - 7}$

Step 4.2

Multiply

2

$2$ by

- 7

$- 7$ .

x = \frac{- 7 \pm \sqrt{301}}{- 14}

$x = \frac{- 7 \pm \sqrt{301}}{- 14}$

Step 4.3

Simplify

\frac{- 7 \pm \sqrt{301}}{- 14}

$\frac{- 7 \pm \sqrt{301}}{- 14}$ .

x = \frac{7 \pm \sqrt{301}}{14}

$x = \frac{7 \pm \sqrt{301}}{14}$

x = \frac{7 \pm \sqrt{301}}{14}

$x = \frac{7 \pm \sqrt{301}}{14}$

Step 5

The result can be shown in multiple forms.

Exact Form:

x = \frac{7 \pm \sqrt{301}}{14}

$x = \frac{7 \pm \sqrt{301}}{14}$

Decimal Form:

x = 1.73923939 \dots, - 0.73923939 \dots

$x = 1.73923939 \dots, - 0.73923939 \dots$