-10x^2+10x+7=0

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Solution for -10x^2+10x+7=0 equation:


Simplifying
-10x2 + 10x + 7 = 0

Reorder the terms:
7 + 10x + -10x2 = 0

Solving
7 + 10x + -10x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-10 the coefficient of the squared term: 

Divide each side by '-10'.
-0.7 + -1x + x2 = 0

Move the constant term to the right:

Add '0.7' to each side of the equation.
-0.7 + -1x + 0.7 + x2 = 0 + 0.7

Reorder the terms:
-0.7 + 0.7 + -1x + x2 = 0 + 0.7

Combine like terms: -0.7 + 0.7 = 0.0
0.0 + -1x + x2 = 0 + 0.7
-1x + x2 = 0 + 0.7

Combine like terms: 0 + 0.7 = 0.7
-1x + x2 = 0.7

The x term is -1x.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1x + 0.25 + x2 = 0.7 + 0.25

Reorder the terms:
0.25 + -1x + x2 = 0.7 + 0.25

Combine like terms: 0.7 + 0.25 = 0.95
0.25 + -1x + x2 = 0.95

Factor a perfect square on the left side:
(x + -0.5)(x + -0.5) = 0.95

Calculate the square root of the right side: 0.974679434

Break this problem into two subproblems by setting 
(x + -0.5) equal to 0.974679434 and -0.974679434.

Subproblem 1

x + -0.5 = 0.974679434 Simplifying x + -0.5 = 0.974679434 Reorder the terms: -0.5 + x = 0.974679434 Solving -0.5 + x = 0.974679434 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 0.974679434 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 0.974679434 + 0.5 x = 0.974679434 + 0.5 Combine like terms: 0.974679434 + 0.5 = 1.474679434 x = 1.474679434 Simplifying x = 1.474679434

Subproblem 2

x + -0.5 = -0.974679434 Simplifying x + -0.5 = -0.974679434 Reorder the terms: -0.5 + x = -0.974679434 Solving -0.5 + x = -0.974679434 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -0.974679434 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -0.974679434 + 0.5 x = -0.974679434 + 0.5 Combine like terms: -0.974679434 + 0.5 = -0.474679434 x = -0.474679434 Simplifying x = -0.474679434

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.474679434, -0.474679434}

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