Algebra Examples

$10 x^{2} + 9 = x$

Step 1

Subtract $x$ from both sides of the equation.

$10 x^{2} + 9 - x = 0$

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 $a = 10$ , $b = - 1$ , and $c = 9$ into the quadratic formula and solve for $x$ .

$\frac{1 \pm \sqrt{{(- 1)}^{2} - 4 \cdot (10 \cdot 9)}}{2 \cdot 10}$

Step 4

Simplify.

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Step 4.1

Simplify the numerator.

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Step 4.1.1

Raise $- 1$ to the power of $2$ .

$x = \frac{1 \pm \sqrt{1 - 4 \cdot 10 \cdot 9}}{2 \cdot 10}$

Step 4.1.2

Multiply $- 4 \cdot 10 \cdot 9$ .

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Step 4.1.2.1

Multiply $- 4$ by $10$ .

$x = \frac{1 \pm \sqrt{1 - 40 \cdot 9}}{2 \cdot 10}$

Step 4.1.2.2

Multiply $- 40$ by $9$ .

$x = \frac{1 \pm \sqrt{1 - 360}}{2 \cdot 10}$

Step 4.1.3

Subtract $360$ from $1$ .

$x = \frac{1 \pm \sqrt{- 359}}{2 \cdot 10}$

Step 4.1.4

Rewrite $- 359$ as $- 1 (359)$ .

$x = \frac{1 \pm \sqrt{- 1 \cdot 359}}{2 \cdot 10}$

Step 4.1.5

Rewrite $\sqrt{- 1 (359)}$ as $\sqrt{- 1} \cdot \sqrt{359}$ .

$x = \frac{1 \pm \sqrt{- 1} \cdot \sqrt{359}}{2 \cdot 10}$

Step 4.1.6

Rewrite $\sqrt{- 1}$ as $i$ .

$x = \frac{1 \pm i \sqrt{359}}{2 \cdot 10}$

Step 4.2

Multiply $2$ by $10$ .

$x = \frac{1 \pm i \sqrt{359}}{20}$