2x^2+3x-5=87

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Solution for 2x^2+3x-5=87 equation:


Simplifying
2x2 + 3x + -5 = 87

Reorder the terms:
-5 + 3x + 2x2 = 87

Solving
-5 + 3x + 2x2 = 87

Solving for variable 'x'.

Reorder the terms:
-5 + -87 + 3x + 2x2 = 87 + -87

Combine like terms: -5 + -87 = -92
-92 + 3x + 2x2 = 87 + -87

Combine like terms: 87 + -87 = 0
-92 + 3x + 2x2 = 0

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

Divide each side by '2'.
-46 + 1.5x + x2 = 0

Move the constant term to the right:

Add '46' to each side of the equation.
-46 + 1.5x + 46 + x2 = 0 + 46

Reorder the terms:
-46 + 46 + 1.5x + x2 = 0 + 46

Combine like terms: -46 + 46 = 0
0 + 1.5x + x2 = 0 + 46
1.5x + x2 = 0 + 46

Combine like terms: 0 + 46 = 46
1.5x + x2 = 46

The x term is 1.5x.  Take half its coefficient (0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
1.5x + 0.5625 + x2 = 46 + 0.5625

Reorder the terms:
0.5625 + 1.5x + x2 = 46 + 0.5625

Combine like terms: 46 + 0.5625 = 46.5625
0.5625 + 1.5x + x2 = 46.5625

Factor a perfect square on the left side:
(x + 0.75)(x + 0.75) = 46.5625

Calculate the square root of the right side: 6.823672032

Break this problem into two subproblems by setting 
(x + 0.75) equal to 6.823672032 and -6.823672032.

Subproblem 1

x + 0.75 = 6.823672032 Simplifying x + 0.75 = 6.823672032 Reorder the terms: 0.75 + x = 6.823672032 Solving 0.75 + x = 6.823672032 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = 6.823672032 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = 6.823672032 + -0.75 x = 6.823672032 + -0.75 Combine like terms: 6.823672032 + -0.75 = 6.073672032 x = 6.073672032 Simplifying x = 6.073672032

Subproblem 2

x + 0.75 = -6.823672032 Simplifying x + 0.75 = -6.823672032 Reorder the terms: 0.75 + x = -6.823672032 Solving 0.75 + x = -6.823672032 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = -6.823672032 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = -6.823672032 + -0.75 x = -6.823672032 + -0.75 Combine like terms: -6.823672032 + -0.75 = -7.573672032 x = -7.573672032 Simplifying x = -7.573672032

Solution

The solution to the problem is based on the solutions from the subproblems. x = {6.073672032, -7.573672032}

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