x*x+10x-1500=0

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Solution for x*x+10x-1500=0 equation:


Simplifying
x * x + 10x + -1500 = 0

Multiply x * x
x2 + 10x + -1500 = 0

Reorder the terms:
-1500 + 10x + x2 = 0

Solving
-1500 + 10x + 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 + 10x + 1500 + x2 = 0 + 1500

Reorder the terms:
-1500 + 1500 + 10x + x2 = 0 + 1500

Combine like terms: -1500 + 1500 = 0
0 + 10x + x2 = 0 + 1500
10x + x2 = 0 + 1500

Combine like terms: 0 + 1500 = 1500
10x + x2 = 1500

The x term is 10x.  Take half its coefficient (5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
10x + 25 + x2 = 1500 + 25

Reorder the terms:
25 + 10x + x2 = 1500 + 25

Combine like terms: 1500 + 25 = 1525
25 + 10x + x2 = 1525

Factor a perfect square on the left side:
(x + 5)(x + 5) = 1525

Calculate the square root of the right side: 39.05124838

Break this problem into two subproblems by setting 
(x + 5) equal to 39.05124838 and -39.05124838.

Subproblem 1

x + 5 = 39.05124838 Simplifying x + 5 = 39.05124838 Reorder the terms: 5 + x = 39.05124838 Solving 5 + x = 39.05124838 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 39.05124838 + -5 Combine like terms: 5 + -5 = 0 0 + x = 39.05124838 + -5 x = 39.05124838 + -5 Combine like terms: 39.05124838 + -5 = 34.05124838 x = 34.05124838 Simplifying x = 34.05124838

Subproblem 2

x + 5 = -39.05124838 Simplifying x + 5 = -39.05124838 Reorder the terms: 5 + x = -39.05124838 Solving 5 + x = -39.05124838 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = -39.05124838 + -5 Combine like terms: 5 + -5 = 0 0 + x = -39.05124838 + -5 x = -39.05124838 + -5 Combine like terms: -39.05124838 + -5 = -44.05124838 x = -44.05124838 Simplifying x = -44.05124838

Solution

The solution to the problem is based on the solutions from the subproblems. x = {34.05124838, -44.05124838}

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