75=50+15x+(x)(x)

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Solution for 75=50+15x+(x)(x) equation:


Simplifying
75 = 50 + 15x + (x)(x)

Multiply x * x
75 = 50 + 15x + x2

Solving
75 = 50 + 15x + x2

Solving for variable 'x'.

Combine like terms: 75 + -50 = 25
25 + -15x + -1x2 = 50 + 15x + x2 + -50 + -15x + -1x2

Reorder the terms:
25 + -15x + -1x2 = 50 + -50 + 15x + -15x + x2 + -1x2

Combine like terms: 50 + -50 = 0
25 + -15x + -1x2 = 0 + 15x + -15x + x2 + -1x2
25 + -15x + -1x2 = 15x + -15x + x2 + -1x2

Combine like terms: 15x + -15x = 0
25 + -15x + -1x2 = 0 + x2 + -1x2
25 + -15x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
25 + -15x + -1x2 = 0

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

Divide each side by '-1'.
-25 + 15x + x2 = 0

Move the constant term to the right:

Add '25' to each side of the equation.
-25 + 15x + 25 + x2 = 0 + 25

Reorder the terms:
-25 + 25 + 15x + x2 = 0 + 25

Combine like terms: -25 + 25 = 0
0 + 15x + x2 = 0 + 25
15x + x2 = 0 + 25

Combine like terms: 0 + 25 = 25
15x + x2 = 25

The x term is 15x.  Take half its coefficient (7.5).
Square it (56.25) and add it to both sides.

Add '56.25' to each side of the equation.
15x + 56.25 + x2 = 25 + 56.25

Reorder the terms:
56.25 + 15x + x2 = 25 + 56.25

Combine like terms: 25 + 56.25 = 81.25
56.25 + 15x + x2 = 81.25

Factor a perfect square on the left side:
(x + 7.5)(x + 7.5) = 81.25

Calculate the square root of the right side: 9.013878189

Break this problem into two subproblems by setting 
(x + 7.5) equal to 9.013878189 and -9.013878189.

Subproblem 1

x + 7.5 = 9.013878189 Simplifying x + 7.5 = 9.013878189 Reorder the terms: 7.5 + x = 9.013878189 Solving 7.5 + x = 9.013878189 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + x = 9.013878189 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = 9.013878189 + -7.5 x = 9.013878189 + -7.5 Combine like terms: 9.013878189 + -7.5 = 1.513878189 x = 1.513878189 Simplifying x = 1.513878189

Subproblem 2

x + 7.5 = -9.013878189 Simplifying x + 7.5 = -9.013878189 Reorder the terms: 7.5 + x = -9.013878189 Solving 7.5 + x = -9.013878189 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + x = -9.013878189 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = -9.013878189 + -7.5 x = -9.013878189 + -7.5 Combine like terms: -9.013878189 + -7.5 = -16.513878189 x = -16.513878189 Simplifying x = -16.513878189

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.513878189, -16.513878189}

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