-4.9x^2+8.5x+130=0

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Solution for -4.9x^2+8.5x+130=0 equation:


Simplifying
-4.9x2 + 8.5x + 130 = 0

Reorder the terms:
130 + 8.5x + -4.9x2 = 0

Solving
130 + 8.5x + -4.9x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-4.9 the coefficient of the squared term: 

Divide each side by '-4.9'.
-26.53061224 + -1.734693878x + x2 = 0

Move the constant term to the right:

Add '26.53061224' to each side of the equation.
-26.53061224 + -1.734693878x + 26.53061224 + x2 = 0 + 26.53061224

Reorder the terms:
-26.53061224 + 26.53061224 + -1.734693878x + x2 = 0 + 26.53061224

Combine like terms: -26.53061224 + 26.53061224 = 0.00000000
0.00000000 + -1.734693878x + x2 = 0 + 26.53061224
-1.734693878x + x2 = 0 + 26.53061224

Combine like terms: 0 + 26.53061224 = 26.53061224
-1.734693878x + x2 = 26.53061224

The x term is -1.734693878x.  Take half its coefficient (-0.867346939).
Square it (0.7522907126) and add it to both sides.

Add '0.7522907126' to each side of the equation.
-1.734693878x + 0.7522907126 + x2 = 26.53061224 + 0.7522907126

Reorder the terms:
0.7522907126 + -1.734693878x + x2 = 26.53061224 + 0.7522907126

Combine like terms: 26.53061224 + 0.7522907126 = 27.2829029526
0.7522907126 + -1.734693878x + x2 = 27.2829029526

Factor a perfect square on the left side:
(x + -0.867346939)(x + -0.867346939) = 27.2829029526

Calculate the square root of the right side: 5.223303835

Break this problem into two subproblems by setting 
(x + -0.867346939) equal to 5.223303835 and -5.223303835.

Subproblem 1

x + -0.867346939 = 5.223303835 Simplifying x + -0.867346939 = 5.223303835 Reorder the terms: -0.867346939 + x = 5.223303835 Solving -0.867346939 + x = 5.223303835 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.867346939' to each side of the equation. -0.867346939 + 0.867346939 + x = 5.223303835 + 0.867346939 Combine like terms: -0.867346939 + 0.867346939 = 0.000000000 0.000000000 + x = 5.223303835 + 0.867346939 x = 5.223303835 + 0.867346939 Combine like terms: 5.223303835 + 0.867346939 = 6.090650774 x = 6.090650774 Simplifying x = 6.090650774

Subproblem 2

x + -0.867346939 = -5.223303835 Simplifying x + -0.867346939 = -5.223303835 Reorder the terms: -0.867346939 + x = -5.223303835 Solving -0.867346939 + x = -5.223303835 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.867346939' to each side of the equation. -0.867346939 + 0.867346939 + x = -5.223303835 + 0.867346939 Combine like terms: -0.867346939 + 0.867346939 = 0.000000000 0.000000000 + x = -5.223303835 + 0.867346939 x = -5.223303835 + 0.867346939 Combine like terms: -5.223303835 + 0.867346939 = -4.355956896 x = -4.355956896 Simplifying x = -4.355956896

Solution

The solution to the problem is based on the solutions from the subproblems. x = {6.090650774, -4.355956896}

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