Solve (x+1)^(2)=(x+2)^(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

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

Solve for x

$x = -\frac{3}{2} = -1\frac{1}{2} = -1.5$

Steps for Solving Linear Equation

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

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

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

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

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

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

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

$$2x+1=4x+4$$

Subtract $4x$ from both sides.

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

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

$$-2x+1=4$$

Subtract $1$ from both sides.

$$-2x=4-1$$

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

$$-2x=3$$

Divide both sides by $-2$.

$$x=\frac{3}{-2}$$

Fraction $\frac{3}{-2}$ can be rewritten as $-\frac{3}{2}$ by extracting the negative sign.

$$x=-\frac{3}{2}$$