5*5+x*x+5*x=1500-26

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Solution for 5*5+x*x+5*x=1500-26 equation:


Simplifying
5 * 5 + x * x + 5x = 1500 + -26

Multiply 5 * 5
25 + x * x + 5x = 1500 + -26

Multiply x * x
25 + x2 + 5x = 1500 + -26

Reorder the terms:
25 + 5x + x2 = 1500 + -26

Combine like terms: 1500 + -26 = 1474
25 + 5x + x2 = 1474

Solving
25 + 5x + x2 = 1474

Solving for variable 'x'.

Reorder the terms:
25 + -1474 + 5x + x2 = 1474 + -1474

Combine like terms: 25 + -1474 = -1449
-1449 + 5x + x2 = 1474 + -1474

Combine like terms: 1474 + -1474 = 0
-1449 + 5x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '1449' to each side of the equation.
-1449 + 5x + 1449 + x2 = 0 + 1449

Reorder the terms:
-1449 + 1449 + 5x + x2 = 0 + 1449

Combine like terms: -1449 + 1449 = 0
0 + 5x + x2 = 0 + 1449
5x + x2 = 0 + 1449

Combine like terms: 0 + 1449 = 1449
5x + x2 = 1449

The x term is 5x.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5x + 6.25 + x2 = 1449 + 6.25

Reorder the terms:
6.25 + 5x + x2 = 1449 + 6.25

Combine like terms: 1449 + 6.25 = 1455.25
6.25 + 5x + x2 = 1455.25

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 1455.25

Calculate the square root of the right side: 38.14773912

Break this problem into two subproblems by setting 
(x + 2.5) equal to 38.14773912 and -38.14773912.

Subproblem 1

x + 2.5 = 38.14773912 Simplifying x + 2.5 = 38.14773912 Reorder the terms: 2.5 + x = 38.14773912 Solving 2.5 + x = 38.14773912 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 38.14773912 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 38.14773912 + -2.5 x = 38.14773912 + -2.5 Combine like terms: 38.14773912 + -2.5 = 35.64773912 x = 35.64773912 Simplifying x = 35.64773912

Subproblem 2

x + 2.5 = -38.14773912 Simplifying x + 2.5 = -38.14773912 Reorder the terms: 2.5 + x = -38.14773912 Solving 2.5 + x = -38.14773912 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -38.14773912 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -38.14773912 + -2.5 x = -38.14773912 + -2.5 Combine like terms: -38.14773912 + -2.5 = -40.64773912 x = -40.64773912 Simplifying x = -40.64773912

Solution

The solution to the problem is based on the solutions from the subproblems. x = {35.64773912, -40.64773912}

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