-5(x)=7x^2-1

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Solution for -5(x)=7x^2-1 equation:


Simplifying
-5(x) = 7x2 + -1

Reorder the terms:
-5x = -1 + 7x2

Solving
-5x = -1 + 7x2

Solving for variable 'x'.

Reorder the terms:
1 + -5x + -7x2 = -1 + 7x2 + 1 + -7x2

Reorder the terms:
1 + -5x + -7x2 = -1 + 1 + 7x2 + -7x2

Combine like terms: -1 + 1 = 0
1 + -5x + -7x2 = 0 + 7x2 + -7x2
1 + -5x + -7x2 = 7x2 + -7x2

Combine like terms: 7x2 + -7x2 = 0
1 + -5x + -7x2 = 0

Begin completing the square.  Divide all terms by
-7 the coefficient of the squared term: 

Divide each side by '-7'.
-0.1428571429 + 0.7142857143x + x2 = 0

Move the constant term to the right:

Add '0.1428571429' to each side of the equation.
-0.1428571429 + 0.7142857143x + 0.1428571429 + x2 = 0 + 0.1428571429

Reorder the terms:
-0.1428571429 + 0.1428571429 + 0.7142857143x + x2 = 0 + 0.1428571429

Combine like terms: -0.1428571429 + 0.1428571429 = 0.0000000000
0.0000000000 + 0.7142857143x + x2 = 0 + 0.1428571429
0.7142857143x + x2 = 0 + 0.1428571429

Combine like terms: 0 + 0.1428571429 = 0.1428571429
0.7142857143x + x2 = 0.1428571429

The x term is 0.7142857143x.  Take half its coefficient (0.3571428572).
Square it (0.1275510204) and add it to both sides.

Add '0.1275510204' to each side of the equation.
0.7142857143x + 0.1275510204 + x2 = 0.1428571429 + 0.1275510204

Reorder the terms:
0.1275510204 + 0.7142857143x + x2 = 0.1428571429 + 0.1275510204

Combine like terms: 0.1428571429 + 0.1275510204 = 0.2704081633
0.1275510204 + 0.7142857143x + x2 = 0.2704081633

Factor a perfect square on the left side:
(x + 0.3571428572)(x + 0.3571428572) = 0.2704081633

Calculate the square root of the right side: 0.520007849

Break this problem into two subproblems by setting 
(x + 0.3571428572) equal to 0.520007849 and -0.520007849.

Subproblem 1

x + 0.3571428572 = 0.520007849 Simplifying x + 0.3571428572 = 0.520007849 Reorder the terms: 0.3571428572 + x = 0.520007849 Solving 0.3571428572 + x = 0.520007849 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3571428572' to each side of the equation. 0.3571428572 + -0.3571428572 + x = 0.520007849 + -0.3571428572 Combine like terms: 0.3571428572 + -0.3571428572 = 0.0000000000 0.0000000000 + x = 0.520007849 + -0.3571428572 x = 0.520007849 + -0.3571428572 Combine like terms: 0.520007849 + -0.3571428572 = 0.1628649918 x = 0.1628649918 Simplifying x = 0.1628649918

Subproblem 2

x + 0.3571428572 = -0.520007849 Simplifying x + 0.3571428572 = -0.520007849 Reorder the terms: 0.3571428572 + x = -0.520007849 Solving 0.3571428572 + x = -0.520007849 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3571428572' to each side of the equation. 0.3571428572 + -0.3571428572 + x = -0.520007849 + -0.3571428572 Combine like terms: 0.3571428572 + -0.3571428572 = 0.0000000000 0.0000000000 + x = -0.520007849 + -0.3571428572 x = -0.520007849 + -0.3571428572 Combine like terms: -0.520007849 + -0.3571428572 = -0.8771507062 x = -0.8771507062 Simplifying x = -0.8771507062

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.1628649918, -0.8771507062}

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