Solve (x + 3) ^ 2 - (x + 1) ^ 2 = 12 | 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

$$(x+3)^{2}-(x+1)^{2}=12$$

Solve for x

$x=1$

Steps for Solving Linear Equation

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

$$x^{2}+6x+9-\left(x+1\right)^{2}=12$$

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

$$x^{2}+6x+9-\left(x^{2}+2x+1\right)=12$$

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

$$x^{2}+6x+9-x^{2}-2x-1=12$$

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

$$6x+9-2x-1=12$$

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

$$4x+9-1=12$$

Subtract $1$ from $9$ to get $8$.

$$4x+8=12$$

Subtract $8$ from both sides.

$$4x=12-8$$

Subtract $8$ from $12$ to get $4$.

$$4x=4$$

Divide both sides by $4$.

$$x=\frac{4}{4}$$

Divide $4$ by $4$ to get $1$.

$$x=1$$