-5x^2+6x+5=0

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Solution for -5x^2+6x+5=0 equation:


Simplifying
-5x2 + 6x + 5 = 0

Reorder the terms:
5 + 6x + -5x2 = 0

Solving
5 + 6x + -5x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-5 the coefficient of the squared term: 

Divide each side by '-5'.
-1 + -1.2x + x2 = 0

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + -1.2x + 1 + x2 = 0 + 1

Reorder the terms:
-1 + 1 + -1.2x + x2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -1.2x + x2 = 0 + 1
-1.2x + x2 = 0 + 1

Combine like terms: 0 + 1 = 1
-1.2x + x2 = 1

The x term is -1.2x.  Take half its coefficient (-0.6).
Square it (0.36) and add it to both sides.

Add '0.36' to each side of the equation.
-1.2x + 0.36 + x2 = 1 + 0.36

Reorder the terms:
0.36 + -1.2x + x2 = 1 + 0.36

Combine like terms: 1 + 0.36 = 1.36
0.36 + -1.2x + x2 = 1.36

Factor a perfect square on the left side:
(x + -0.6)(x + -0.6) = 1.36

Calculate the square root of the right side: 1.166190379

Break this problem into two subproblems by setting 
(x + -0.6) equal to 1.166190379 and -1.166190379.

Subproblem 1

x + -0.6 = 1.166190379 Simplifying x + -0.6 = 1.166190379 Reorder the terms: -0.6 + x = 1.166190379 Solving -0.6 + x = 1.166190379 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6' to each side of the equation. -0.6 + 0.6 + x = 1.166190379 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + x = 1.166190379 + 0.6 x = 1.166190379 + 0.6 Combine like terms: 1.166190379 + 0.6 = 1.766190379 x = 1.766190379 Simplifying x = 1.766190379

Subproblem 2

x + -0.6 = -1.166190379 Simplifying x + -0.6 = -1.166190379 Reorder the terms: -0.6 + x = -1.166190379 Solving -0.6 + x = -1.166190379 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6' to each side of the equation. -0.6 + 0.6 + x = -1.166190379 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + x = -1.166190379 + 0.6 x = -1.166190379 + 0.6 Combine like terms: -1.166190379 + 0.6 = -0.566190379 x = -0.566190379 Simplifying x = -0.566190379

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.766190379, -0.566190379}

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