-7x=10x^2-8

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Solution for -7x=10x^2-8 equation:


Simplifying
-7x = 10x2 + -8

Reorder the terms:
-7x = -8 + 10x2

Solving
-7x = -8 + 10x2

Solving for variable 'x'.

Reorder the terms:
8 + -7x + -10x2 = -8 + 10x2 + 8 + -10x2

Reorder the terms:
8 + -7x + -10x2 = -8 + 8 + 10x2 + -10x2

Combine like terms: -8 + 8 = 0
8 + -7x + -10x2 = 0 + 10x2 + -10x2
8 + -7x + -10x2 = 10x2 + -10x2

Combine like terms: 10x2 + -10x2 = 0
8 + -7x + -10x2 = 0

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

Divide each side by '-10'.
-0.8 + 0.7x + x2 = 0

Move the constant term to the right:

Add '0.8' to each side of the equation.
-0.8 + 0.7x + 0.8 + x2 = 0 + 0.8

Reorder the terms:
-0.8 + 0.8 + 0.7x + x2 = 0 + 0.8

Combine like terms: -0.8 + 0.8 = 0.0
0.0 + 0.7x + x2 = 0 + 0.8
0.7x + x2 = 0 + 0.8

Combine like terms: 0 + 0.8 = 0.8
0.7x + x2 = 0.8

The x term is 0.7x.  Take half its coefficient (0.35).
Square it (0.1225) and add it to both sides.

Add '0.1225' to each side of the equation.
0.7x + 0.1225 + x2 = 0.8 + 0.1225

Reorder the terms:
0.1225 + 0.7x + x2 = 0.8 + 0.1225

Combine like terms: 0.8 + 0.1225 = 0.9225
0.1225 + 0.7x + x2 = 0.9225

Factor a perfect square on the left side:
(x + 0.35)(x + 0.35) = 0.9225

Calculate the square root of the right side: 0.960468636

Break this problem into two subproblems by setting 
(x + 0.35) equal to 0.960468636 and -0.960468636.

Subproblem 1

x + 0.35 = 0.960468636 Simplifying x + 0.35 = 0.960468636 Reorder the terms: 0.35 + x = 0.960468636 Solving 0.35 + x = 0.960468636 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.35' to each side of the equation. 0.35 + -0.35 + x = 0.960468636 + -0.35 Combine like terms: 0.35 + -0.35 = 0.00 0.00 + x = 0.960468636 + -0.35 x = 0.960468636 + -0.35 Combine like terms: 0.960468636 + -0.35 = 0.610468636 x = 0.610468636 Simplifying x = 0.610468636

Subproblem 2

x + 0.35 = -0.960468636 Simplifying x + 0.35 = -0.960468636 Reorder the terms: 0.35 + x = -0.960468636 Solving 0.35 + x = -0.960468636 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.35' to each side of the equation. 0.35 + -0.35 + x = -0.960468636 + -0.35 Combine like terms: 0.35 + -0.35 = 0.00 0.00 + x = -0.960468636 + -0.35 x = -0.960468636 + -0.35 Combine like terms: -0.960468636 + -0.35 = -1.310468636 x = -1.310468636 Simplifying x = -1.310468636

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.610468636, -1.310468636}

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