(2x-5)(x)=35

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Solution for (2x-5)(x)=35 equation:


Simplifying
(2x + -5)(x) = 35

Reorder the terms:
(-5 + 2x)(x) = 35

Reorder the terms for easier multiplication:
x(-5 + 2x) = 35
(-5 * x + 2x * x) = 35
(-5x + 2x2) = 35

Solving
-5x + 2x2 = 35

Solving for variable 'x'.

Reorder the terms:
-35 + -5x + 2x2 = 35 + -35

Combine like terms: 35 + -35 = 0
-35 + -5x + 2x2 = 0

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

Divide each side by '2'.
-17.5 + -2.5x + x2 = 0

Move the constant term to the right:

Add '17.5' to each side of the equation.
-17.5 + -2.5x + 17.5 + x2 = 0 + 17.5

Reorder the terms:
-17.5 + 17.5 + -2.5x + x2 = 0 + 17.5

Combine like terms: -17.5 + 17.5 = 0.0
0.0 + -2.5x + x2 = 0 + 17.5
-2.5x + x2 = 0 + 17.5

Combine like terms: 0 + 17.5 = 17.5
-2.5x + x2 = 17.5

The x term is -2.5x.  Take half its coefficient (-1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
-2.5x + 1.5625 + x2 = 17.5 + 1.5625

Reorder the terms:
1.5625 + -2.5x + x2 = 17.5 + 1.5625

Combine like terms: 17.5 + 1.5625 = 19.0625
1.5625 + -2.5x + x2 = 19.0625

Factor a perfect square on the left side:
(x + -1.25)(x + -1.25) = 19.0625

Calculate the square root of the right side: 4.366062299

Break this problem into two subproblems by setting 
(x + -1.25) equal to 4.366062299 and -4.366062299.

Subproblem 1

x + -1.25 = 4.366062299 Simplifying x + -1.25 = 4.366062299 Reorder the terms: -1.25 + x = 4.366062299 Solving -1.25 + x = 4.366062299 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = 4.366062299 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = 4.366062299 + 1.25 x = 4.366062299 + 1.25 Combine like terms: 4.366062299 + 1.25 = 5.616062299 x = 5.616062299 Simplifying x = 5.616062299

Subproblem 2

x + -1.25 = -4.366062299 Simplifying x + -1.25 = -4.366062299 Reorder the terms: -1.25 + x = -4.366062299 Solving -1.25 + x = -4.366062299 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = -4.366062299 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = -4.366062299 + 1.25 x = -4.366062299 + 1.25 Combine like terms: -4.366062299 + 1.25 = -3.116062299 x = -3.116062299 Simplifying x = -3.116062299

Solution

The solution to the problem is based on the solutions from the subproblems. x = {5.616062299, -3.116062299}

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