5*8x+x^2=85

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Solution for 5*8x+x^2=85 equation:


Simplifying
5 * 8x + x2 = 85

Multiply 5 * 8
40x + x2 = 85

Solving
40x + x2 = 85

Solving for variable 'x'.

Reorder the terms:
-85 + 40x + x2 = 85 + -85

Combine like terms: 85 + -85 = 0
-85 + 40x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '85' to each side of the equation.
-85 + 40x + 85 + x2 = 0 + 85

Reorder the terms:
-85 + 85 + 40x + x2 = 0 + 85

Combine like terms: -85 + 85 = 0
0 + 40x + x2 = 0 + 85
40x + x2 = 0 + 85

Combine like terms: 0 + 85 = 85
40x + x2 = 85

The x term is 40x.  Take half its coefficient (20).
Square it (400) and add it to both sides.

Add '400' to each side of the equation.
40x + 400 + x2 = 85 + 400

Reorder the terms:
400 + 40x + x2 = 85 + 400

Combine like terms: 85 + 400 = 485
400 + 40x + x2 = 485

Factor a perfect square on the left side:
(x + 20)(x + 20) = 485

Calculate the square root of the right side: 22.022715546

Break this problem into two subproblems by setting 
(x + 20) equal to 22.022715546 and -22.022715546.

Subproblem 1

x + 20 = 22.022715546 Simplifying x + 20 = 22.022715546 Reorder the terms: 20 + x = 22.022715546 Solving 20 + x = 22.022715546 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-20' to each side of the equation. 20 + -20 + x = 22.022715546 + -20 Combine like terms: 20 + -20 = 0 0 + x = 22.022715546 + -20 x = 22.022715546 + -20 Combine like terms: 22.022715546 + -20 = 2.022715546 x = 2.022715546 Simplifying x = 2.022715546

Subproblem 2

x + 20 = -22.022715546 Simplifying x + 20 = -22.022715546 Reorder the terms: 20 + x = -22.022715546 Solving 20 + x = -22.022715546 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-20' to each side of the equation. 20 + -20 + x = -22.022715546 + -20 Combine like terms: 20 + -20 = 0 0 + x = -22.022715546 + -20 x = -22.022715546 + -20 Combine like terms: -22.022715546 + -20 = -42.022715546 x = -42.022715546 Simplifying x = -42.022715546

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.022715546, -42.022715546}

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