(15+20)15=(x+26)x

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Solution for (15+20)15=(x+26)x equation:


Simplifying
(15 + 20) * 15 = (x + 26) * x

Combine like terms: 15 + 20 = 35
(35) * 15 = (x + 26) * x

Multiply 35 * 15
525 = (x + 26) * x

Reorder the terms:
525 = (26 + x) * x

Reorder the terms for easier multiplication:
525 = x(26 + x)
525 = (26 * x + x * x)
525 = (26x + x2)

Solving
525 = 26x + x2

Solving for variable 'x'.

Reorder the terms:
525 + -26x + -1x2 = 26x + -26x + x2 + -1x2

Combine like terms: 26x + -26x = 0
525 + -26x + -1x2 = 0 + x2 + -1x2
525 + -26x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
525 + -26x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-525 + 26x + x2 = 0

Move the constant term to the right:

Add '525' to each side of the equation.
-525 + 26x + 525 + x2 = 0 + 525

Reorder the terms:
-525 + 525 + 26x + x2 = 0 + 525

Combine like terms: -525 + 525 = 0
0 + 26x + x2 = 0 + 525
26x + x2 = 0 + 525

Combine like terms: 0 + 525 = 525
26x + x2 = 525

The x term is 26x.  Take half its coefficient (13).
Square it (169) and add it to both sides.

Add '169' to each side of the equation.
26x + 169 + x2 = 525 + 169

Reorder the terms:
169 + 26x + x2 = 525 + 169

Combine like terms: 525 + 169 = 694
169 + 26x + x2 = 694

Factor a perfect square on the left side:
(x + 13)(x + 13) = 694

Calculate the square root of the right side: 26.343879745

Break this problem into two subproblems by setting 
(x + 13) equal to 26.343879745 and -26.343879745.

Subproblem 1

x + 13 = 26.343879745 Simplifying x + 13 = 26.343879745 Reorder the terms: 13 + x = 26.343879745 Solving 13 + x = 26.343879745 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + x = 26.343879745 + -13 Combine like terms: 13 + -13 = 0 0 + x = 26.343879745 + -13 x = 26.343879745 + -13 Combine like terms: 26.343879745 + -13 = 13.343879745 x = 13.343879745 Simplifying x = 13.343879745

Subproblem 2

x + 13 = -26.343879745 Simplifying x + 13 = -26.343879745 Reorder the terms: 13 + x = -26.343879745 Solving 13 + x = -26.343879745 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + x = -26.343879745 + -13 Combine like terms: 13 + -13 = 0 0 + x = -26.343879745 + -13 x = -26.343879745 + -13 Combine like terms: -26.343879745 + -13 = -39.343879745 x = -39.343879745 Simplifying x = -39.343879745

Solution

The solution to the problem is based on the solutions from the subproblems. x = {13.343879745, -39.343879745}

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