-0.026x^2+0.512x+5=6

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Solution for -0.026x^2+0.512x+5=6 equation:


Simplifying
-0.026x2 + 0.512x + 5 = 6

Reorder the terms:
5 + 0.512x + -0.026x2 = 6

Solving
5 + 0.512x + -0.026x2 = 6

Solving for variable 'x'.

Reorder the terms:
5 + -6 + 0.512x + -0.026x2 = 6 + -6

Combine like terms: 5 + -6 = -1
-1 + 0.512x + -0.026x2 = 6 + -6

Combine like terms: 6 + -6 = 0
-1 + 0.512x + -0.026x2 = 0

Begin completing the square.  Divide all terms by
-0.026 the coefficient of the squared term: 

Divide each side by '-0.026'.
38.46153846 + -19.69230769x + x2 = 0

Move the constant term to the right:

Add '-38.46153846' to each side of the equation.
38.46153846 + -19.69230769x + -38.46153846 + x2 = 0 + -38.46153846

Reorder the terms:
38.46153846 + -38.46153846 + -19.69230769x + x2 = 0 + -38.46153846

Combine like terms: 38.46153846 + -38.46153846 = 0.00000000
0.00000000 + -19.69230769x + x2 = 0 + -38.46153846
-19.69230769x + x2 = 0 + -38.46153846

Combine like terms: 0 + -38.46153846 = -38.46153846
-19.69230769x + x2 = -38.46153846

The x term is -19.69230769x.  Take half its coefficient (-9.846153845).
Square it (96.94674554) and add it to both sides.

Add '96.94674554' to each side of the equation.
-19.69230769x + 96.94674554 + x2 = -38.46153846 + 96.94674554

Reorder the terms:
96.94674554 + -19.69230769x + x2 = -38.46153846 + 96.94674554

Combine like terms: -38.46153846 + 96.94674554 = 58.48520708
96.94674554 + -19.69230769x + x2 = 58.48520708

Factor a perfect square on the left side:
(x + -9.846153845)(x + -9.846153845) = 58.48520708

Calculate the square root of the right side: 7.647562166

Break this problem into two subproblems by setting 
(x + -9.846153845) equal to 7.647562166 and -7.647562166.

Subproblem 1

x + -9.846153845 = 7.647562166 Simplifying x + -9.846153845 = 7.647562166 Reorder the terms: -9.846153845 + x = 7.647562166 Solving -9.846153845 + x = 7.647562166 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.846153845' to each side of the equation. -9.846153845 + 9.846153845 + x = 7.647562166 + 9.846153845 Combine like terms: -9.846153845 + 9.846153845 = 0.000000000 0.000000000 + x = 7.647562166 + 9.846153845 x = 7.647562166 + 9.846153845 Combine like terms: 7.647562166 + 9.846153845 = 17.493716011 x = 17.493716011 Simplifying x = 17.493716011

Subproblem 2

x + -9.846153845 = -7.647562166 Simplifying x + -9.846153845 = -7.647562166 Reorder the terms: -9.846153845 + x = -7.647562166 Solving -9.846153845 + x = -7.647562166 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.846153845' to each side of the equation. -9.846153845 + 9.846153845 + x = -7.647562166 + 9.846153845 Combine like terms: -9.846153845 + 9.846153845 = 0.000000000 0.000000000 + x = -7.647562166 + 9.846153845 x = -7.647562166 + 9.846153845 Combine like terms: -7.647562166 + 9.846153845 = 2.198591679 x = 2.198591679 Simplifying x = 2.198591679

Solution

The solution to the problem is based on the solutions from the subproblems. x = {17.493716011, 2.198591679}

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