Pre-Algebra Examples

$25 x^{2} - 64 x + 18 y - 71 = 0$

Step 1

Use the quadratic formula to find the solutions.

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

Step 2

Substitute the values $a = 25$ , $b = - 64$ , and $c = 18 y - 71$ into the quadratic formula and solve for $x$ .

$\frac{64 \pm \sqrt{{(- 64)}^{2} - 4 \cdot (25 \cdot (18 y - 71))}}{2 \cdot 25}$

Step 3

Simplify.

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Step 3.1

Simplify the numerator.

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Step 3.1.1

Raise $- 64$ to the power of $2$ .

$x = \frac{64 \pm \sqrt{4096 - 4 \cdot 25 \cdot (18 y - 71)}}{2 \cdot 25}$

Step 3.1.2

Multiply $- 4$ by $25$ .

$x = \frac{64 \pm \sqrt{4096 - 100 \cdot (18 y - 71)}}{2 \cdot 25}$

Step 3.1.3

Apply the distributive property.

$x = \frac{64 \pm \sqrt{4096 - 100 (18 y) - 100 \cdot - 71}}{2 \cdot 25}$

Step 3.1.4

Multiply $18$ by $- 100$ .

$x = \frac{64 \pm \sqrt{4096 - 1800 y - 100 \cdot - 71}}{2 \cdot 25}$

Step 3.1.5

Multiply $- 100$ by $- 71$ .

$x = \frac{64 \pm \sqrt{4096 - 1800 y + 7100}}{2 \cdot 25}$

Step 3.1.6

Add $4096$ and $7100$ .

$x = \frac{64 \pm \sqrt{- 1800 y + 11196}}{2 \cdot 25}$

Step 3.1.7

Factor $36$ out of $- 1800 y + 11196$ .

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Step 3.1.7.1

Factor $36$ out of $- 1800 y$ .

$x = \frac{64 \pm \sqrt{36 (- 50 y) + 11196}}{2 \cdot 25}$

Step 3.1.7.2

Factor $36$ out of $11196$ .

$x = \frac{64 \pm \sqrt{36 (- 50 y) + 36 (311)}}{2 \cdot 25}$

Step 3.1.7.3

Factor $36$ out of $36 (- 50 y) + 36 (311)$ .

$x = \frac{64 \pm \sqrt{36 (- 50 y + 311)}}{2 \cdot 25}$

Step 3.1.8

Rewrite $36$ as $6^{2}$ .

$x = \frac{64 \pm \sqrt{6^{2} (- 50 y + 311)}}{2 \cdot 25}$

Step 3.1.9

Pull terms out from under the radical.

$x = \frac{64 \pm 6 \sqrt{- 50 y + 311}}{2 \cdot 25}$

Step 3.2

Multiply $2$ by $25$ .

$x = \frac{64 \pm 6 \sqrt{- 50 y + 311}}{50}$

Step 3.3

Simplify $\frac{64 \pm 6 \sqrt{- 50 y + 311}}{50}$ .

$x = \frac{32 \pm 3 \sqrt{- 50 y + 311}}{25}$

Step 4

The final answer is the combination of both solutions.

$x = \frac{32 + 3 \sqrt{- 50 y + 311}}{25}$

$x = \frac{32 - 3 \sqrt{- 50 y + 311}}{25}$