-2x^2+3x+50=0

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Solution for -2x^2+3x+50=0 equation:


Simplifying
-2x2 + 3x + 50 = 0

Reorder the terms:
50 + 3x + -2x2 = 0

Solving
50 + 3x + -2x2 = 0

Solving for variable 'x'.

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

Divide each side by '-2'.
-25 + -1.5x + x2 = 0

Move the constant term to the right:

Add '25' to each side of the equation.
-25 + -1.5x + 25 + x2 = 0 + 25

Reorder the terms:
-25 + 25 + -1.5x + x2 = 0 + 25

Combine like terms: -25 + 25 = 0
0 + -1.5x + x2 = 0 + 25
-1.5x + x2 = 0 + 25

Combine like terms: 0 + 25 = 25
-1.5x + x2 = 25

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 = 25 + 0.5625

Reorder the terms:
0.5625 + -1.5x + x2 = 25 + 0.5625

Combine like terms: 25 + 0.5625 = 25.5625
0.5625 + -1.5x + x2 = 25.5625

Factor a perfect square on the left side:
(x + -0.75)(x + -0.75) = 25.5625

Calculate the square root of the right side: 5.055937104

Break this problem into two subproblems by setting 
(x + -0.75) equal to 5.055937104 and -5.055937104.

Subproblem 1

x + -0.75 = 5.055937104 Simplifying x + -0.75 = 5.055937104 Reorder the terms: -0.75 + x = 5.055937104 Solving -0.75 + x = 5.055937104 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 = 5.055937104 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = 5.055937104 + 0.75 x = 5.055937104 + 0.75 Combine like terms: 5.055937104 + 0.75 = 5.805937104 x = 5.805937104 Simplifying x = 5.805937104

Subproblem 2

x + -0.75 = -5.055937104 Simplifying x + -0.75 = -5.055937104 Reorder the terms: -0.75 + x = -5.055937104 Solving -0.75 + x = -5.055937104 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 = -5.055937104 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = -5.055937104 + 0.75 x = -5.055937104 + 0.75 Combine like terms: -5.055937104 + 0.75 = -4.305937104 x = -4.305937104 Simplifying x = -4.305937104

Solution

The solution to the problem is based on the solutions from the subproblems. x = {5.805937104, -4.305937104}

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