Solve しゅ 24x(x + 4) = 4x ^ 2 - pi | Equatix - Math Solver

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Example

3(r+2s)=2t-4

a⋅(b-2)=3b

3(r+2s)=2t-4

a⋅(b-2)=3b

Question

$$24 x ( x + 1 ) = 4 x ^ { 2 } - 2$$

Solve for x

$x=\frac{\sqrt{26}}{10}-\frac{3}{5}\approx -0.090098049$
$x=-\frac{\sqrt{26}}{10}-\frac{3}{5}\approx -1.109901951$

Steps Using the Quadratic Formula

Steps for Completing the Square

Steps Using the Quadratic Formula

Use the distributive property to multiply $24x$ by $x+1$.

$$24x^{2}+24x=4x^{2}-2$$

Subtract $4x^{2}$ from both sides.

$$24x^{2}+24x-4x^{2}=-2$$

Combine $24x^{2}$ and $-4x^{2}$ to get $20x^{2}$.

$$20x^{2}+24x=-2$$

Add $2$ to both sides.

$$20x^{2}+24x+2=0$$

This equation is in standard form: $ax^{2}+bx+c=0$. Substitute $20$ for $a$, $24$ for $b$, and $2$ for $c$ in the quadratic formula, $\frac{-b±\sqrt{b^{2}-4ac}}{2a}$.

$$x=\frac{-24±\sqrt{24^{2}-4\times 20\times 2}}{2\times 20}$$

Square $24$.

$$x=\frac{-24±\sqrt{576-4\times 20\times 2}}{2\times 20}$$

Multiply $-4$ times $20$.

$$x=\frac{-24±\sqrt{576-80\times 2}}{2\times 20}$$

Multiply $-80$ times $2$.

$$x=\frac{-24±\sqrt{576-160}}{2\times 20}$$

Add $576$ to $-160$.

$$x=\frac{-24±\sqrt{416}}{2\times 20}$$

Take the square root of $416$.

$$x=\frac{-24±4\sqrt{26}}{2\times 20}$$

Multiply $2$ times $20$.

$$x=\frac{-24±4\sqrt{26}}{40}$$

Now solve the equation $x=\frac{-24±4\sqrt{26}}{40}$ when $±$ is plus. Add $-24$ to $4\sqrt{26}$.

$$x=\frac{4\sqrt{26}-24}{40}$$

Divide $-24+4\sqrt{26}$ by $40$.

$$x=\frac{\sqrt{26}}{10}-\frac{3}{5}$$

Now solve the equation $x=\frac{-24±4\sqrt{26}}{40}$ when $±$ is minus. Subtract $4\sqrt{26}$ from $-24$.

$$x=\frac{-4\sqrt{26}-24}{40}$$

Divide $-24-4\sqrt{26}$ by $40$.

$$x=-\frac{\sqrt{26}}{10}-\frac{3}{5}$$

The equation is now solved.

$$x=\frac{\sqrt{26}}{10}-\frac{3}{5}$$ $$x=-\frac{\sqrt{26}}{10}-\frac{3}{5}$$

Steps for Completing the Square

Use the distributive property to multiply $24x$ by $x+1$.

$$24x^{2}+24x=4x^{2}-2$$

Subtract $4x^{2}$ from both sides.

$$24x^{2}+24x-4x^{2}=-2$$

Combine $24x^{2}$ and $-4x^{2}$ to get $20x^{2}$.

$$20x^{2}+24x=-2$$

Divide both sides by $20$.

$$\frac{20x^{2}+24x}{20}=-\frac{2}{20}$$

Dividing by $20$ undoes the multiplication by $20$.

$$x^{2}+\frac{24}{20}x=-\frac{2}{20}$$

Reduce the fraction $\frac{24}{20}$ to lowest terms by extracting and canceling out $4$.

$$x^{2}+\frac{6}{5}x=-\frac{2}{20}$$

Reduce the fraction $\frac{-2}{20}$ to lowest terms by extracting and canceling out $2$.

$$x^{2}+\frac{6}{5}x=-\frac{1}{10}$$

Divide $\frac{6}{5}$, the coefficient of the $x$ term, by $2$ to get $\frac{3}{5}$. Then add the square of $\frac{3}{5}$ to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}+\frac{6}{5}x+\left(\frac{3}{5}\right)^{2}=-\frac{1}{10}+\left(\frac{3}{5}\right)^{2}$$

Square $\frac{3}{5}$ by squaring both the numerator and the denominator of the fraction.

$$x^{2}+\frac{6}{5}x+\frac{9}{25}=-\frac{1}{10}+\frac{9}{25}$$

Add $-\frac{1}{10}$ to $\frac{9}{25}$ by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.

$$x^{2}+\frac{6}{5}x+\frac{9}{25}=\frac{13}{50}$$

Factor $x^{2}+\frac{6}{5}x+\frac{9}{25}$. In general, when $x^{2}+bx+c$ is a perfect square, it can always be factored as $\left(x+\frac{b}{2}\right)^{2}$.

$$\left(x+\frac{3}{5}\right)^{2}=\frac{13}{50}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x+\frac{3}{5}\right)^{2}}=\sqrt{\frac{13}{50}}$$

Simplify.

$$x+\frac{3}{5}=\frac{\sqrt{26}}{10}$$ $$x+\frac{3}{5}=-\frac{\sqrt{26}}{10}$$

Subtract $\frac{3}{5}$ from both sides of the equation.

$$x=\frac{\sqrt{26}}{10}-\frac{3}{5}$$ $$x=-\frac{\sqrt{26}}{10}-\frac{3}{5}$$