Solve (x - 3) ^ 2 - (x + 2) ^ 2 = - 25 | 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

$$(x-3)^{2}-(x+2)^{2}=-25$$

Solve for x

$x=3$

Steps for Solving Linear Equation

Use binomial theorem $\left(a-b\right)^{2}=a^{2}-2ab+b^{2}$ to expand $\left(x-3\right)^{2}$.

$$x^{2}-6x+9-\left(x+2\right)^{2}=-25$$

Use binomial theorem $\left(a+b\right)^{2}=a^{2}+2ab+b^{2}$ to expand $\left(x+2\right)^{2}$.

$$x^{2}-6x+9-\left(x^{2}+4x+4\right)=-25$$

To find the opposite of $x^{2}+4x+4$, find the opposite of each term.

$$x^{2}-6x+9-x^{2}-4x-4=-25$$

Combine $x^{2}$ and $-x^{2}$ to get $0$.

$$-6x+9-4x-4=-25$$

Combine $-6x$ and $-4x$ to get $-10x$.

$$-10x+9-4=-25$$

Subtract $4$ from $9$ to get $5$.

$$-10x+5=-25$$

Subtract $5$ from both sides.

$$-10x=-25-5$$

Subtract $5$ from $-25$ to get $-30$.

$$-10x=-30$$

Divide both sides by $-10$.

$$x=\frac{-30}{-10}$$

Divide $-30$ by $-10$ to get $3$.

$$x=3$$