Solve (x - 1) ^ 2 - (x - 2) ^ 2 = 5 | 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

$$(x-1)^{2}-(x-2)^{2}=5$$

Solve for x

$x=4$

Steps for Solving Linear Equation

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

$$x^{2}-2x+1-\left(x-2\right)^{2}=5$$

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

$$x^{2}-2x+1-\left(x^{2}-4x+4\right)=5$$

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

$$x^{2}-2x+1-x^{2}+4x-4=5$$

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

$$-2x+1+4x-4=5$$

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

$$2x+1-4=5$$

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

$$2x-3=5$$

Add $3$ to both sides.

$$2x=5+3$$

Add $5$ and $3$ to get $8$.

$$2x=8$$

Divide both sides by $2$.

$$x=\frac{8}{2}$$

Divide $8$ by $2$ to get $4$.

$$x=4$$