Pre-Algebra Examples

${(9 \sqrt{x})}^{2} - 43 x = 76$

Step 1

Simplify ${(9 \sqrt{x})}^{2} - 43 x$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the product rule to $9 \sqrt{x}$ .

$9^{2} {\sqrt{x}}^{2} - 43 x = 76$

Step 1.1.2

Raise $9$ to the power of $2$ .

$81 {\sqrt{x}}^{2} - 43 x = 76$

Step 1.1.3

Rewrite ${\sqrt{x}}^{2}$ as $x$ .

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Step 1.1.3.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{x}$ as $x^{\frac{1}{2}}$ .

$81 {(x^{\frac{1}{2}})}^{2} - 43 x = 76$

Step 1.1.3.2

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$81 x^{\frac{1}{2} \cdot 2} - 43 x = 76$

Step 1.1.3.3

Combine $\frac{1}{2}$ and $2$ .

$81 x^{\frac{2}{2}} - 43 x = 76$

Step 1.1.3.4

Cancel the common factor of $2$ .

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Step 1.1.3.4.1

Cancel the common factor.

$81 x^{\frac{2}{2}} - 43 x = 76$

Step 1.1.3.4.2

Rewrite the expression.

$81 x^{1} - 43 x = 76$

Step 1.1.3.5

Simplify.

$81 x - 43 x = 76$

Step 1.2

Subtract $43 x$ from $81 x$ .

$38 x = 76$

Step 2

Graph each side of the equation. The solution is the x-value of the point of intersection.

$x = 2$

Step 3