(2x*2x)-15x=8

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Solution for (2x*2x)-15x=8 equation:


Simplifying
(2x * 2x) + -15x = 8

Reorder the terms for easier multiplication:
(2 * 2x * x) + -15x = 8

Multiply 2 * 2
(4x * x) + -15x = 8

Multiply x * x
(4x2) + -15x = 8

Reorder the terms:
-15x + (4x2) = 8

Solving
-15x + (4x2) = 8

Solving for variable 'x'.

Reorder the terms:
-8 + -15x + (4x2) = 8 + -8

Combine like terms: 8 + -8 = 0
-8 + -15x + (4x2) = 0

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

Divide each side by '4'.
-2 + -3.75x + x2 = 0

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + -3.75x + 2 + x2 = 0 + 2

Reorder the terms:
-2 + 2 + -3.75x + x2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -3.75x + x2 = 0 + 2
-3.75x + x2 = 0 + 2

Combine like terms: 0 + 2 = 2
-3.75x + x2 = 2

The x term is -3.75x.  Take half its coefficient (-1.875).
Square it (3.515625) and add it to both sides.

Add '3.515625' to each side of the equation.
-3.75x + 3.515625 + x2 = 2 + 3.515625

Reorder the terms:
3.515625 + -3.75x + x2 = 2 + 3.515625

Combine like terms: 2 + 3.515625 = 5.515625
3.515625 + -3.75x + x2 = 5.515625

Factor a perfect square on the left side:
((x) + -1.875)((x) + -1.875) = 5.515625

Calculate the square root of the right side: 2.348536779

Break this problem into two subproblems by setting 
((x) + -1.875) equal to 2.348536779 and -2.348536779.

Subproblem 1

(x) + -1.875 = 2.348536779 Simplifying (x) + -1.875 = 2.348536779 x + -1.875 = 2.348536779 Reorder the terms: -1.875 + x = 2.348536779 Solving -1.875 + x = 2.348536779 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.875' to each side of the equation. -1.875 + 1.875 + x = 2.348536779 + 1.875 Combine like terms: -1.875 + 1.875 = 0.000 0.000 + x = 2.348536779 + 1.875 x = 2.348536779 + 1.875 Combine like terms: 2.348536779 + 1.875 = 4.223536779 x = 4.223536779 Simplifying x = 4.223536779

Subproblem 2

(x) + -1.875 = -2.348536779 Simplifying (x) + -1.875 = -2.348536779 x + -1.875 = -2.348536779 Reorder the terms: -1.875 + x = -2.348536779 Solving -1.875 + x = -2.348536779 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.875' to each side of the equation. -1.875 + 1.875 + x = -2.348536779 + 1.875 Combine like terms: -1.875 + 1.875 = 0.000 0.000 + x = -2.348536779 + 1.875 x = -2.348536779 + 1.875 Combine like terms: -2.348536779 + 1.875 = -0.473536779 x = -0.473536779 Simplifying x = -0.473536779

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4.223536779, -0.473536779}

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