2x^2-5x=142

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Solution for 2x^2-5x=142 equation:


Simplifying
2x2 + -5x = 142

Reorder the terms:
-5x + 2x2 = 142

Solving
-5x + 2x2 = 142

Solving for variable 'x'.

Reorder the terms:
-142 + -5x + 2x2 = 142 + -142

Combine like terms: 142 + -142 = 0
-142 + -5x + 2x2 = 0

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

Divide each side by '2'.
-71 + -2.5x + x2 = 0

Move the constant term to the right:

Add '71' to each side of the equation.
-71 + -2.5x + 71 + x2 = 0 + 71

Reorder the terms:
-71 + 71 + -2.5x + x2 = 0 + 71

Combine like terms: -71 + 71 = 0
0 + -2.5x + x2 = 0 + 71
-2.5x + x2 = 0 + 71

Combine like terms: 0 + 71 = 71
-2.5x + x2 = 71

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 = 71 + 1.5625

Reorder the terms:
1.5625 + -2.5x + x2 = 71 + 1.5625

Combine like terms: 71 + 1.5625 = 72.5625
1.5625 + -2.5x + x2 = 72.5625

Factor a perfect square on the left side:
(x + -1.25)(x + -1.25) = 72.5625

Calculate the square root of the right side: 8.518362519

Break this problem into two subproblems by setting 
(x + -1.25) equal to 8.518362519 and -8.518362519.

Subproblem 1

x + -1.25 = 8.518362519 Simplifying x + -1.25 = 8.518362519 Reorder the terms: -1.25 + x = 8.518362519 Solving -1.25 + x = 8.518362519 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 = 8.518362519 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = 8.518362519 + 1.25 x = 8.518362519 + 1.25 Combine like terms: 8.518362519 + 1.25 = 9.768362519 x = 9.768362519 Simplifying x = 9.768362519

Subproblem 2

x + -1.25 = -8.518362519 Simplifying x + -1.25 = -8.518362519 Reorder the terms: -1.25 + x = -8.518362519 Solving -1.25 + x = -8.518362519 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 = -8.518362519 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = -8.518362519 + 1.25 x = -8.518362519 + 1.25 Combine like terms: -8.518362519 + 1.25 = -7.268362519 x = -7.268362519 Simplifying x = -7.268362519

Solution

The solution to the problem is based on the solutions from the subproblems. x = {9.768362519, -7.268362519}

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