Algebra Examples

$x^{2} + 72 - 1200 = 0$

Step 1

Simplify the left side.

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Step 1.1

Subtract $1200$ from $72$ .

$x^{2} - 1128 = 0$

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 $a = 1$ , $b = 0$ , and $c = - 1128$ into the quadratic formula and solve for $x$ .

$\frac{0 \pm \sqrt{0^{2} - 4 \cdot (1 \cdot - 1128)}}{2 \cdot 1}$

Step 4

Simplify.

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Step 4.1

Simplify the numerator.

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Step 4.1.1

Raising $0$ to any positive power yields $0$ .

$x = \frac{0 \pm \sqrt{0 - 4 \cdot 1 \cdot - 1128}}{2 \cdot 1}$

Step 4.1.2

Multiply $- 4 \cdot 1 \cdot - 1128$ .

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Step 4.1.2.1

Multiply $- 4$ by $1$ .

$x = \frac{0 \pm \sqrt{0 - 4 \cdot - 1128}}{2 \cdot 1}$

Step 4.1.2.2

Multiply $- 4$ by $- 1128$ .

$x = \frac{0 \pm \sqrt{0 + 4512}}{2 \cdot 1}$

Step 4.1.3

Add $0$ and $4512$ .

$x = \frac{0 \pm \sqrt{4512}}{2 \cdot 1}$

Step 4.1.4

Rewrite $4512$ as $4^{2} \cdot 282$ .

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Step 4.1.4.1

Factor $16$ out of $4512$ .

$x = \frac{0 \pm \sqrt{16 (282)}}{2 \cdot 1}$

Step 4.1.4.2

Rewrite $16$ as $4^{2}$ .

$x = \frac{0 \pm \sqrt{4^{2} \cdot 282}}{2 \cdot 1}$

Step 4.1.5

Pull terms out from under the radical.

$x = \frac{0 \pm 4 \sqrt{282}}{2 \cdot 1}$

Step 4.2

Multiply $2$ by $1$ .

$x = \frac{0 \pm 4 \sqrt{282}}{2}$

Step 4.3

Simplify $\frac{0 \pm 4 \sqrt{282}}{2}$ .

$x = \pm 2 \sqrt{282}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \pm 2 \sqrt{282}$

Decimal Form:

$x = 33.58571124 \dots, - 33.58571124 \dots$