40x^2-7x-3500=1500

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Solution for 40x^2-7x-3500=1500 equation: 


Simplifying
40x2 + -7x + -3500 = 1500

Reorder the terms:
-3500 + -7x + 40x2 = 1500

Solving
-3500 + -7x + 40x2 = 1500

Solving for variable 'x'.

Reorder the terms:
-3500 + -1500 + -7x + 40x2 = 1500 + -1500

Combine like terms: -3500 + -1500 = -5000
-5000 + -7x + 40x2 = 1500 + -1500

Combine like terms: 1500 + -1500 = 0
-5000 + -7x + 40x2 = 0

Begin completing the square.  Divide all terms by
40 the coefficient of the squared term: 

Divide each side by '40'.
-125 + -0.175x + x2 = 0

Move the constant term to the right:

Add '125' to each side of the equation.
-125 + -0.175x + 125 + x2 = 0 + 125

Reorder the terms:
-125 + 125 + -0.175x + x2 = 0 + 125

Combine like terms: -125 + 125 = 0
0 + -0.175x + x2 = 0 + 125
-0.175x + x2 = 0 + 125

Combine like terms: 0 + 125 = 125
-0.175x + x2 = 125

The x term is -0.175x.  Take half its coefficient (-0.0875).
Square it (0.00765625) and add it to both sides.

Add '0.00765625' to each side of the equation.
-0.175x + 0.00765625 + x2 = 125 + 0.00765625

Reorder the terms:
0.00765625 + -0.175x + x2 = 125 + 0.00765625

Combine like terms: 125 + 0.00765625 = 125.00765625
0.00765625 + -0.175x + x2 = 125.00765625

Factor a perfect square on the left side:
(x + -0.0875)(x + -0.0875) = 125.00765625

Calculate the square root of the right side: 11.18068228

Break this problem into two subproblems by setting 
(x + -0.0875) equal to 11.18068228 and -11.18068228.


Subproblem 1
x + -0.0875 = 11.18068228

Simplifying
x + -0.0875 = 11.18068228

Reorder the terms:
-0.0875 + x = 11.18068228

Solving
-0.0875 + x = 11.18068228

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '0.0875' to each side of the equation.
-0.0875 + 0.0875 + x = 11.18068228 + 0.0875

Combine like terms: -0.0875 + 0.0875 = 0.0000
0.0000 + x = 11.18068228 + 0.0875
x = 11.18068228 + 0.0875

Combine like terms: 11.18068228 + 0.0875 = 11.26818228
x = 11.26818228

Simplifying
x = 11.26818228


Subproblem 2
x + -0.0875 = -11.18068228

Simplifying
x + -0.0875 = -11.18068228

Reorder the terms:
-0.0875 + x = -11.18068228

Solving
-0.0875 + x = -11.18068228

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '0.0875' to each side of the equation.
-0.0875 + 0.0875 + x = -11.18068228 + 0.0875

Combine like terms: -0.0875 + 0.0875 = 0.0000
0.0000 + x = -11.18068228 + 0.0875
x = -11.18068228 + 0.0875

Combine like terms: -11.18068228 + 0.0875 = -11.09318228
x = -11.09318228

Simplifying
x = -11.09318228


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {11.26818228, -11.09318228}

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