Solve (x + 2) ^ 2 - (x - 1) ^ 2 = 15 | 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

$$(x+2)^{2}-(x-1)^{2}=15$$

Solve for x

$x=2$

Steps for Solving Linear Equation

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

$$x^{2}+4x+4-\left(x-1\right)^{2}=15$$

Use binomial theorem $\left(a-b\right)^{2}=a^{2}-2ab+b^{2}$ to expand $\left(x-1\right)^{2}$.

$$x^{2}+4x+4-\left(x^{2}-2x+1\right)=15$$

To find the opposite of $x^{2}-2x+1$, find the opposite of each term.

$$x^{2}+4x+4-x^{2}+2x-1=15$$

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

$$4x+4+2x-1=15$$

Combine $4x$ and $2x$ to get $6x$.

$$6x+4-1=15$$

Subtract $1$ from $4$ to get $3$.

$$6x+3=15$$

Subtract $3$ from both sides.

$$6x=15-3$$

Subtract $3$ from $15$ to get $12$.

$$6x=12$$

Divide both sides by $6$.

$$x=\frac{12}{6}$$

Divide $12$ by $6$ to get $2$.

$$x=2$$