5x^2+7x-130=0

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Solution for 5x^2+7x-130=0 equation:


Simplifying
5x2 + 7x + -130 = 0

Reorder the terms:
-130 + 7x + 5x2 = 0

Solving
-130 + 7x + 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'.
-26 + 1.4x + x2 = 0

Move the constant term to the right:

Add '26' to each side of the equation.
-26 + 1.4x + 26 + x2 = 0 + 26

Reorder the terms:
-26 + 26 + 1.4x + x2 = 0 + 26

Combine like terms: -26 + 26 = 0
0 + 1.4x + x2 = 0 + 26
1.4x + x2 = 0 + 26

Combine like terms: 0 + 26 = 26
1.4x + x2 = 26

The x term is 1.4x.  Take half its coefficient (0.7).
Square it (0.49) and add it to both sides.

Add '0.49' to each side of the equation.
1.4x + 0.49 + x2 = 26 + 0.49

Reorder the terms:
0.49 + 1.4x + x2 = 26 + 0.49

Combine like terms: 26 + 0.49 = 26.49
0.49 + 1.4x + x2 = 26.49

Factor a perfect square on the left side:
(x + 0.7)(x + 0.7) = 26.49

Calculate the square root of the right side: 5.146843693

Break this problem into two subproblems by setting 
(x + 0.7) equal to 5.146843693 and -5.146843693.

Subproblem 1

x + 0.7 = 5.146843693 Simplifying x + 0.7 = 5.146843693 Reorder the terms: 0.7 + x = 5.146843693 Solving 0.7 + x = 5.146843693 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.7' to each side of the equation. 0.7 + -0.7 + x = 5.146843693 + -0.7 Combine like terms: 0.7 + -0.7 = 0.0 0.0 + x = 5.146843693 + -0.7 x = 5.146843693 + -0.7 Combine like terms: 5.146843693 + -0.7 = 4.446843693 x = 4.446843693 Simplifying x = 4.446843693

Subproblem 2

x + 0.7 = -5.146843693 Simplifying x + 0.7 = -5.146843693 Reorder the terms: 0.7 + x = -5.146843693 Solving 0.7 + x = -5.146843693 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.7' to each side of the equation. 0.7 + -0.7 + x = -5.146843693 + -0.7 Combine like terms: 0.7 + -0.7 = 0.0 0.0 + x = -5.146843693 + -0.7 x = -5.146843693 + -0.7 Combine like terms: -5.146843693 + -0.7 = -5.846843693 x = -5.846843693 Simplifying x = -5.846843693

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4.446843693, -5.846843693}

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