Solve y=05(x+2.4)^2+0.8(2x+7.65)

$$y = 05 ( x + 2.4 ) ^ { 2 } + 0.8 ( 2 x + 7.65 )$$

Solve for x

$$x=\frac{5y}{8}-3.825$$

Steps for Solving Linear Equation

Multiply 0 and 5 to get 0.

$$y=0\left(x+2.4\right)^{2}+0.8\left(2x+7.65\right)$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+2.4\right)^{2}.

$$y=0\left(x^{2}+4.8x+5.76\right)+0.8\left(2x+7.65\right)$$

Anything times zero gives zero.

$$y=0+0.8\left(2x+7.65\right)$$

Use the distributive property to multiply 0.8 by 2x+7.65.

$$y=0+1.6x+6.12$$

Add 0 and 6.12 to get 6.12.

$$y=6.12+1.6x$$

Swap sides so that all variable terms are on the left hand side.

$$6.12+1.6x=y$$

Subtract 6.12 from both sides.

$$1.6x=y-6.12$$

Divide both sides of the equation by 1.6, which is the same as multiplying both sides by the reciprocal of the fraction.

$$\frac{1.6x}{1.6}=\frac{y-6.12}{1.6}$$

Dividing by 1.6 undoes the multiplication by 1.6.

$$x=\frac{y-6.12}{1.6}$$

Divide y-6.12 by 1.6 by multiplying y-6.12 by the reciprocal of 1.6.

$$x=\frac{5y}{8}-3.825$$

Solve for y

$$y=\frac{8x}{5}+6.12$$

Solution Steps

Multiply 0 and 5 to get 0.

$$y=0\left(x+2.4\right)^{2}+0.8\left(2x+7.65\right)$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+2.4\right)^{2}.

$$y=0\left(x^{2}+4.8x+5.76\right)+0.8\left(2x+7.65\right)$$

Anything times zero gives zero.

$$y=0+0.8\left(2x+7.65\right)$$

Use the distributive property to multiply 0.8 by 2x+7.65.

$$y=0+1.6x+6.12$$

Add 0 and 6.12 to get 6.12.

$$y=6.12+1.6x$$