Solve 7(x-4)^(2)-3(x+5)^(2)=4(x+1)(x-1)-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

$$7 { \left(x-4 \right) }^{ 2 } -3 { \left(x+5 \right) }^{ 2 } =4(x+1)(x-1)-2$$

Solve for x

$x=\frac{1}{2}=0.5$

Steps for Solving Linear Equation

Use binomial theorem $\left(a-b\right)^{2}=a^{2}-2ab+b^{2}$ to expand $\left(x-4\right)^{2}$.

$$7\left(x^{2}-8x+16\right)-3\left(x+5\right)^{2}=4\left(x+1\right)\left(x-1\right)-2$$

Use the distributive property to multiply $7$ by $x^{2}-8x+16$.

$$7x^{2}-56x+112-3\left(x+5\right)^{2}=4\left(x+1\right)\left(x-1\right)-2$$

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

$$7x^{2}-56x+112-3\left(x^{2}+10x+25\right)=4\left(x+1\right)\left(x-1\right)-2$$

Use the distributive property to multiply $-3$ by $x^{2}+10x+25$.

$$7x^{2}-56x+112-3x^{2}-30x-75=4\left(x+1\right)\left(x-1\right)-2$$

Combine $7x^{2}$ and $-3x^{2}$ to get $4x^{2}$.

$$4x^{2}-56x+112-30x-75=4\left(x+1\right)\left(x-1\right)-2$$

Combine $-56x$ and $-30x$ to get $-86x$.

$$4x^{2}-86x+112-75=4\left(x+1\right)\left(x-1\right)-2$$

Subtract $75$ from $112$ to get $37$.

$$4x^{2}-86x+37=4\left(x+1\right)\left(x-1\right)-2$$

Use the distributive property to multiply $4$ by $x+1$.

$$4x^{2}-86x+37=\left(4x+4\right)\left(x-1\right)-2$$

Use the distributive property to multiply $4x+4$ by $x-1$ and combine like terms.

$$4x^{2}-86x+37=4x^{2}-4-2$$

Subtract $2$ from $-4$ to get $-6$.

$$4x^{2}-86x+37=4x^{2}-6$$

Subtract $4x^{2}$ from both sides.

$$4x^{2}-86x+37-4x^{2}=-6$$

Combine $4x^{2}$ and $-4x^{2}$ to get $0$.

$$-86x+37=-6$$

Subtract $37$ from both sides.

$$-86x=-6-37$$

Subtract $37$ from $-6$ to get $-43$.

$$-86x=-43$$

Divide both sides by $-86$.

$$x=\frac{-43}{-86}$$

Reduce the fraction $\frac{-43}{-86}$ to lowest terms by extracting and canceling out $-43$.

$$x=\frac{1}{2}$$