Solve (x+4)^(2)-(x-5)^(2)=9 | 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

$${ \left(x+4 \right) }^{ 2 } - { \left(x-5 \right) }^{ 2 } =9$$

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 $\left(x+4\right)^{2}$.

$$x^{2}+8x+16-\left(x-5\right)^{2}=9$$

Use binomial theorem $\left(a-b\right)^{2}=a^{2}-2ab+b^{2}$ to expand $\left(x-5\right)^{2}$.

$$x^{2}+8x+16-\left(x^{2}-10x+25\right)=9$$

To find the opposite of $x^{2}-10x+25$, find the opposite of each term.

$$x^{2}+8x+16-x^{2}+10x-25=9$$

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

$$8x+16+10x-25=9$$

Combine $8x$ and $10x$ to get $18x$.

$$18x+16-25=9$$

Subtract $25$ from $16$ to get $-9$.

$$18x-9=9$$

Add $9$ to both sides.

$$18x=9+9$$

Add $9$ and $9$ to get $18$.

$$18x=18$$

Divide both sides by $18$.

$$x=\frac{18}{18}$$

Divide $18$ by $18$ to get $1$.

$$x=1$$