Solve (x)^(2)-(1)^(2)=2(x)^(2)-(7)^(2) | 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

$${ x }^{ 2 } - { 1 }^{ 2 } =2 { x }^{ 2 } - { 7 }^{ 2 }$$

Solve for x

$x=4\sqrt{3}\approx 6.92820323$
$x=-4\sqrt{3}\approx -6.92820323$

Steps by Finding Square Root

Steps Using the Quadratic Formula

Steps by Finding Square Root

Calculate $1$ to the power of $2$ and get $1$.

$$x^{2}-1=2x^{2}-7^{2}$$

Calculate $7$ to the power of $2$ and get $49$.

$$x^{2}-1=2x^{2}-49$$

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

$$x^{2}-1-2x^{2}=-49$$

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

$$-x^{2}-1=-49$$

Add $1$ to both sides.

$$-x^{2}=-49+1$$

Add $-49$ and $1$ to get $-48$.

$$-x^{2}=-48$$

Divide both sides by $-1$.

$$x^{2}=\frac{-48}{-1}$$

Fraction $\frac{-48}{-1}$ can be simplified to $48$ by removing the negative sign from both the numerator and the denominator.

$$x^{2}=48$$

Take the square root of both sides of the equation.

$$x=4\sqrt{3}$$ $$x=-4\sqrt{3}$$

Steps Using the Quadratic Formula

Calculate $1$ to the power of $2$ and get $1$.

$$x^{2}-1=2x^{2}-7^{2}$$

Calculate $7$ to the power of $2$ and get $49$.

$$x^{2}-1=2x^{2}-49$$

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

$$x^{2}-1-2x^{2}=-49$$

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

$$-x^{2}-1=-49$$

Add $49$ to both sides.

$$-x^{2}-1+49=0$$

Add $-1$ and $49$ to get $48$.

$$-x^{2}+48=0$$

This equation is in standard form: $ax^{2}+bx+c=0$. Substitute $-1$ for $a$, $0$ for $b$, and $48$ for $c$ in the quadratic formula, $\frac{-b±\sqrt{b^{2}-4ac}}{2a}$.

$$x=\frac{0±\sqrt{0^{2}-4\left(-1\right)\times 48}}{2\left(-1\right)}$$

Square $0$.

$$x=\frac{0±\sqrt{-4\left(-1\right)\times 48}}{2\left(-1\right)}$$

Multiply $-4$ times $-1$.

$$x=\frac{0±\sqrt{4\times 48}}{2\left(-1\right)}$$

Multiply $4$ times $48$.

$$x=\frac{0±\sqrt{192}}{2\left(-1\right)}$$

Take the square root of $192$.

$$x=\frac{0±8\sqrt{3}}{2\left(-1\right)}$$

Multiply $2$ times $-1$.

$$x=\frac{0±8\sqrt{3}}{-2}$$

Now solve the equation $x=\frac{0±8\sqrt{3}}{-2}$ when $±$ is plus.

$$x=-4\sqrt{3}$$

Now solve the equation $x=\frac{0±8\sqrt{3}}{-2}$ when $±$ is minus.

$$x=4\sqrt{3}$$

The equation is now solved.

$$x=-4\sqrt{3}$$ $$x=4\sqrt{3}$$