Solve A=(x-2)(3-5)+(3x-5)(3x+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

$$A=(x-2)(3-5)+(3x-5)(3x+5)$$

Solve for A

$A=9x^{2}-2x-21$

Solution Steps

Subtract $5$ from $3$ to get $-2$.

$$A=\left(x-2\right)\left(-2\right)+\left(3x-5\right)\left(3x+5\right)$$

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

$$A=-2x+4+\left(3x-5\right)\left(3x+5\right)$$

Consider $\left(3x-5\right)\left(3x+5\right)$. Multiplication can be transformed into difference of squares using the rule: $\left(a-b\right)\left(a+b\right)=a^{2}-b^{2}$. Square $5$.

$$A=-2x+4+\left(3x\right)^{2}-25$$

Expand $\left(3x\right)^{2}$.

$$A=-2x+4+3^{2}x^{2}-25$$

Calculate $3$ to the power of $2$ and get $9$.

$$A=-2x+4+9x^{2}-25$$

Subtract $25$ from $4$ to get $-21$.

$$A=-2x-21+9x^{2}$$

Solve for x (complex solution)

$x=\frac{-\sqrt{9A+190}+1}{9}$
$x=\frac{\sqrt{9A+190}+1}{9}$

Solve for x

$x=\frac{-\sqrt{9A+190}+1}{9}$
$x=\frac{\sqrt{9A+190}+1}{9}\text{, }A\geq -\frac{190}{9}$