x=-10x^2+6x+7

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Solution for x=-10x^2+6x+7 equation:


Simplifying
x = -10x2 + 6x + 7

Reorder the terms:
x = 7 + 6x + -10x2

Solving
x = 7 + 6x + -10x2

Solving for variable 'x'.

Reorder the terms:
-7 + x + -6x + 10x2 = 7 + 6x + -10x2 + -7 + -6x + 10x2

Combine like terms: x + -6x = -5x
-7 + -5x + 10x2 = 7 + 6x + -10x2 + -7 + -6x + 10x2

Reorder the terms:
-7 + -5x + 10x2 = 7 + -7 + 6x + -6x + -10x2 + 10x2

Combine like terms: 7 + -7 = 0
-7 + -5x + 10x2 = 0 + 6x + -6x + -10x2 + 10x2
-7 + -5x + 10x2 = 6x + -6x + -10x2 + 10x2

Combine like terms: 6x + -6x = 0
-7 + -5x + 10x2 = 0 + -10x2 + 10x2
-7 + -5x + 10x2 = -10x2 + 10x2

Combine like terms: -10x2 + 10x2 = 0
-7 + -5x + 10x2 = 0

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

Divide each side by '10'.
-0.7 + -0.5x + x2 = 0

Move the constant term to the right:

Add '0.7' to each side of the equation.
-0.7 + -0.5x + 0.7 + x2 = 0 + 0.7

Reorder the terms:
-0.7 + 0.7 + -0.5x + x2 = 0 + 0.7

Combine like terms: -0.7 + 0.7 = 0.0
0.0 + -0.5x + x2 = 0 + 0.7
-0.5x + x2 = 0 + 0.7

Combine like terms: 0 + 0.7 = 0.7
-0.5x + x2 = 0.7

The x term is -0.5x.  Take half its coefficient (-0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
-0.5x + 0.0625 + x2 = 0.7 + 0.0625

Reorder the terms:
0.0625 + -0.5x + x2 = 0.7 + 0.0625

Combine like terms: 0.7 + 0.0625 = 0.7625
0.0625 + -0.5x + x2 = 0.7625

Factor a perfect square on the left side:
(x + -0.25)(x + -0.25) = 0.7625

Calculate the square root of the right side: 0.87321246

Break this problem into two subproblems by setting 
(x + -0.25) equal to 0.87321246 and -0.87321246.

Subproblem 1

x + -0.25 = 0.87321246 Simplifying x + -0.25 = 0.87321246 Reorder the terms: -0.25 + x = 0.87321246 Solving -0.25 + x = 0.87321246 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = 0.87321246 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = 0.87321246 + 0.25 x = 0.87321246 + 0.25 Combine like terms: 0.87321246 + 0.25 = 1.12321246 x = 1.12321246 Simplifying x = 1.12321246

Subproblem 2

x + -0.25 = -0.87321246 Simplifying x + -0.25 = -0.87321246 Reorder the terms: -0.25 + x = -0.87321246 Solving -0.25 + x = -0.87321246 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = -0.87321246 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = -0.87321246 + 0.25 x = -0.87321246 + 0.25 Combine like terms: -0.87321246 + 0.25 = -0.62321246 x = -0.62321246 Simplifying x = -0.62321246

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.12321246, -0.62321246}

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