Solve 3 * (x - 4) ^ 2 + 5 * (x - 3) ^ 2 = (2x - 5)(4x - 1) - 40 | 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

$$3(x-4)^{2}+5(x-3)^{2}=(2x-5)(4x-1)-40$$

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

$$3\left(x^{2}-8x+16\right)+5\left(x-3\right)^{2}=\left(2x-5\right)\left(4x-1\right)-40$$

Use the distributive property to multiply $3$ by $x^{2}-8x+16$.

$$3x^{2}-24x+48+5\left(x-3\right)^{2}=\left(2x-5\right)\left(4x-1\right)-40$$

Use binomial theorem $\left(a-b\right)^{2}=a^{2}-2ab+b^{2}$ to expand $\left(x-3\right)^{2}$.

$$3x^{2}-24x+48+5\left(x^{2}-6x+9\right)=\left(2x-5\right)\left(4x-1\right)-40$$

Use the distributive property to multiply $5$ by $x^{2}-6x+9$.

$$3x^{2}-24x+48+5x^{2}-30x+45=\left(2x-5\right)\left(4x-1\right)-40$$

Combine $3x^{2}$ and $5x^{2}$ to get $8x^{2}$.

$$8x^{2}-24x+48-30x+45=\left(2x-5\right)\left(4x-1\right)-40$$

Combine $-24x$ and $-30x$ to get $-54x$.

$$8x^{2}-54x+48+45=\left(2x-5\right)\left(4x-1\right)-40$$

Add $48$ and $45$ to get $93$.

$$8x^{2}-54x+93=\left(2x-5\right)\left(4x-1\right)-40$$

Use the distributive property to multiply $2x-5$ by $4x-1$ and combine like terms.

$$8x^{2}-54x+93=8x^{2}-22x+5-40$$

Subtract $40$ from $5$ to get $-35$.

$$8x^{2}-54x+93=8x^{2}-22x-35$$

Subtract $8x^{2}$ from both sides.

$$8x^{2}-54x+93-8x^{2}=-22x-35$$

Combine $8x^{2}$ and $-8x^{2}$ to get $0$.

$$-54x+93=-22x-35$$

Add $22x$ to both sides.

$$-54x+93+22x=-35$$

Combine $-54x$ and $22x$ to get $-32x$.

$$-32x+93=-35$$

Subtract $93$ from both sides.

$$-32x=-35-93$$

Subtract $93$ from $-35$ to get $-128$.

$$-32x=-128$$

Divide both sides by $-32$.

$$x=\frac{-128}{-32}$$

Divide $-128$ by $-32$ to get $4$.

$$x=4$$