x^2+-40x-1500=0

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Solution for x^2+-40x-1500=0 equation:


Simplifying
x2 + -40x + -1500 = 0

Reorder the terms:
-1500 + -40x + x2 = 0

Solving
-1500 + -40x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '1500' to each side of the equation.
-1500 + -40x + 1500 + x2 = 0 + 1500

Reorder the terms:
-1500 + 1500 + -40x + x2 = 0 + 1500

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

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

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 = 1500 + 400

Reorder the terms:
400 + -40x + x2 = 1500 + 400

Combine like terms: 1500 + 400 = 1900
400 + -40x + x2 = 1900

Factor a perfect square on the left side:
(x + -20)(x + -20) = 1900

Calculate the square root of the right side: 43.588989435

Break this problem into two subproblems by setting 
(x + -20) equal to 43.588989435 and -43.588989435.

Subproblem 1

x + -20 = 43.588989435 Simplifying x + -20 = 43.588989435 Reorder the terms: -20 + x = 43.588989435 Solving -20 + x = 43.588989435 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 = 43.588989435 + 20 Combine like terms: -20 + 20 = 0 0 + x = 43.588989435 + 20 x = 43.588989435 + 20 Combine like terms: 43.588989435 + 20 = 63.588989435 x = 63.588989435 Simplifying x = 63.588989435

Subproblem 2

x + -20 = -43.588989435 Simplifying x + -20 = -43.588989435 Reorder the terms: -20 + x = -43.588989435 Solving -20 + x = -43.588989435 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 = -43.588989435 + 20 Combine like terms: -20 + 20 = 0 0 + x = -43.588989435 + 20 x = -43.588989435 + 20 Combine like terms: -43.588989435 + 20 = -23.588989435 x = -23.588989435 Simplifying x = -23.588989435

Solution

The solution to the problem is based on the solutions from the subproblems. x = {63.588989435, -23.588989435}

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