Solve 4 x ^ { 2 } + 7 = 7 + 24 x | Equatix - Math Solver

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Example

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

a⋅(b-2)=3b

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a⋅(b-2)=3b

Question

$$4 x ^ { 2 } + 7 = 7 + 24 x$$

Solve for x

$x=6$
$x=0$

Steps Using Factoring

Steps Using the Quadratic Formula

Steps for Completing the Square

Steps Using Factoring

Subtract $7$ from both sides.

$$4x^{2}+7-7=24x$$

Subtract $7$ from $7$ to get $0$.

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

Subtract $24x$ from both sides.

$$4x^{2}-24x=0$$

Factor out $x$.

$$x\left(4x-24\right)=0$$

To find equation solutions, solve $x=0$ and $4x-24=0$.

$$x=0$$ $$x=6$$

Steps Using the Quadratic Formula

Subtract $7$ from both sides.

$$4x^{2}+7-7=24x$$

Subtract $7$ from $7$ to get $0$.

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

Subtract $24x$ from both sides.

$$4x^{2}-24x=0$$

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

$$x=\frac{-\left(-24\right)±\sqrt{\left(-24\right)^{2}}}{2\times 4}$$

Take the square root of $\left(-24\right)^{2}$.

$$x=\frac{-\left(-24\right)±24}{2\times 4}$$

The opposite of $-24$ is $24$.

$$x=\frac{24±24}{2\times 4}$$

Multiply $2$ times $4$.

$$x=\frac{24±24}{8}$$

Now solve the equation $x=\frac{24±24}{8}$ when $±$ is plus. Add $24$ to $24$.

$$x=\frac{48}{8}$$

Divide $48$ by $8$.

$$x=6$$

Now solve the equation $x=\frac{24±24}{8}$ when $±$ is minus. Subtract $24$ from $24$.

$$x=\frac{0}{8}$$

Divide $0$ by $8$.

$$x=0$$

The equation is now solved.

$$x=6$$ $$x=0$$

Steps for Completing the Square

Subtract $24x$ from both sides.

$$4x^{2}+7-24x=7$$

Subtract $7$ from both sides.

$$4x^{2}-24x=7-7$$

Subtract $7$ from $7$ to get $0$.

$$4x^{2}-24x=0$$

Divide both sides by $4$.

$$\frac{4x^{2}-24x}{4}=\frac{0}{4}$$

Dividing by $4$ undoes the multiplication by $4$.

$$x^{2}+\left(-\frac{24}{4}\right)x=\frac{0}{4}$$

Divide $-24$ by $4$.

$$x^{2}-6x=\frac{0}{4}$$

Divide $0$ by $4$.

$$x^{2}-6x=0$$

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

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

Square $-3$.

$$x^{2}-6x+9=9$$

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

$$\left(x-3\right)^{2}=9$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x-3\right)^{2}}=\sqrt{9}$$

Simplify.

$$x-3=3$$ $$x-3=-3$$

Add $3$ to both sides of the equation.

$$x=6$$ $$x=0$$