Solve A = 2(x - 2)(- x ^ 2 - x + 3) - (- 2x - 1) * (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

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

Solve for A

$A=-\left(x-2\right)\left(5x-4\right)$

Solution Steps

Use the distributive property to multiply $2$ by $x-2$.

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

Use the distributive property to multiply $2x-4$ by $-x^{2}-x+3$ and combine like terms.

$$A=2x\left(-x^{2}\right)-2x^{2}+10x-4\left(-x^{2}\right)-12-\left(-2x-1\right)\left(x-2\right)^{2}$$

Multiply $-4$ and $-1$ to get $4$.

$$A=2x\left(-x^{2}\right)-2x^{2}+10x+4x^{2}-12-\left(-2x-1\right)\left(x-2\right)^{2}$$

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

$$A=2x\left(-x^{2}\right)+2x^{2}+10x-12-\left(-2x-1\right)\left(x-2\right)^{2}$$

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

$$A=2x\left(-x^{2}\right)+2x^{2}+10x-12-\left(-2x-1\right)\left(x^{2}-4x+4\right)$$

Use the distributive property to multiply $-2x-1$ by $x^{2}-4x+4$ and combine like terms.

$$A=2x\left(-x^{2}\right)+2x^{2}+10x-12-\left(-2x^{3}+7x^{2}-4x-4\right)$$

To find the opposite of $-2x^{3}+7x^{2}-4x-4$, find the opposite of each term.

$$A=2x\left(-x^{2}\right)+2x^{2}+10x-12+2x^{3}-7x^{2}+4x+4$$

Combine $2x^{2}$ and $-7x^{2}$ to get $-5x^{2}$.

$$A=2x\left(-x^{2}\right)-5x^{2}+10x-12+2x^{3}+4x+4$$

Combine $10x$ and $4x$ to get $14x$.

$$A=2x\left(-x^{2}\right)-5x^{2}+14x-12+2x^{3}+4$$

Add $-12$ and $4$ to get $-8$.

$$A=2x\left(-x^{2}\right)-5x^{2}+14x-8+2x^{3}$$

To multiply powers of the same base, add their exponents. Add $1$ and $2$ to get $3$.

$$A=2x^{3}\left(-1\right)-5x^{2}+14x-8+2x^{3}$$

Multiply $2$ and $-1$ to get $-2$.

$$A=-2x^{3}-5x^{2}+14x-8+2x^{3}$$

Combine $-2x^{3}$ and $2x^{3}$ to get $0$.

$$A=-5x^{2}+14x-8$$

Solve for x (complex solution)

$x=\frac{\sqrt{9-5A}+7}{5}$
$x=\frac{-\sqrt{9-5A}+7}{5}$

Solve for x

$x=\frac{\sqrt{9-5A}+7}{5}$
$x=\frac{-\sqrt{9-5A}+7}{5}\text{, }A\leq \frac{9}{5}$