35*5=x(4+x)

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Solution for 35*5=x(4+x) equation:


Simplifying
35 * 5 = x(4 + x)

Multiply 35 * 5
175 = x(4 + x)
175 = (4 * x + x * x)
175 = (4x + x2)

Solving
175 = 4x + x2

Solving for variable 'x'.

Reorder the terms:
175 + -4x + -1x2 = 4x + -4x + x2 + -1x2

Combine like terms: 4x + -4x = 0
175 + -4x + -1x2 = 0 + x2 + -1x2
175 + -4x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
175 + -4x + -1x2 = 0

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

Divide each side by '-1'.
-175 + 4x + x2 = 0

Move the constant term to the right:

Add '175' to each side of the equation.
-175 + 4x + 175 + x2 = 0 + 175

Reorder the terms:
-175 + 175 + 4x + x2 = 0 + 175

Combine like terms: -175 + 175 = 0
0 + 4x + x2 = 0 + 175
4x + x2 = 0 + 175

Combine like terms: 0 + 175 = 175
4x + x2 = 175

The x term is 4x.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4x + 4 + x2 = 175 + 4

Reorder the terms:
4 + 4x + x2 = 175 + 4

Combine like terms: 175 + 4 = 179
4 + 4x + x2 = 179

Factor a perfect square on the left side:
(x + 2)(x + 2) = 179

Calculate the square root of the right side: 13.37908816

Break this problem into two subproblems by setting 
(x + 2) equal to 13.37908816 and -13.37908816.

Subproblem 1

x + 2 = 13.37908816 Simplifying x + 2 = 13.37908816 Reorder the terms: 2 + x = 13.37908816 Solving 2 + x = 13.37908816 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 13.37908816 + -2 Combine like terms: 2 + -2 = 0 0 + x = 13.37908816 + -2 x = 13.37908816 + -2 Combine like terms: 13.37908816 + -2 = 11.37908816 x = 11.37908816 Simplifying x = 11.37908816

Subproblem 2

x + 2 = -13.37908816 Simplifying x + 2 = -13.37908816 Reorder the terms: 2 + x = -13.37908816 Solving 2 + x = -13.37908816 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -13.37908816 + -2 Combine like terms: 2 + -2 = 0 0 + x = -13.37908816 + -2 x = -13.37908816 + -2 Combine like terms: -13.37908816 + -2 = -15.37908816 x = -15.37908816 Simplifying x = -15.37908816

Solution

The solution to the problem is based on the solutions from the subproblems. x = {11.37908816, -15.37908816}

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