5x^2+7x-2=

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


Simplifying
5x2 + 7x + -2 = 0

Reorder the terms:
-2 + 7x + 5x2 = 0

Solving
-2 + 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'.
-0.4 + 1.4x + x2 = 0

Move the constant term to the right:

Add '0.4' to each side of the equation.
-0.4 + 1.4x + 0.4 + x2 = 0 + 0.4

Reorder the terms:
-0.4 + 0.4 + 1.4x + x2 = 0 + 0.4

Combine like terms: -0.4 + 0.4 = 0.0
0.0 + 1.4x + x2 = 0 + 0.4
1.4x + x2 = 0 + 0.4

Combine like terms: 0 + 0.4 = 0.4
1.4x + x2 = 0.4

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 = 0.4 + 0.49

Reorder the terms:
0.49 + 1.4x + x2 = 0.4 + 0.49

Combine like terms: 0.4 + 0.49 = 0.89
0.49 + 1.4x + x2 = 0.89

Factor a perfect square on the left side:
(x + 0.7)(x + 0.7) = 0.89

Calculate the square root of the right side: 0.943398113

Break this problem into two subproblems by setting 
(x + 0.7) equal to 0.943398113 and -0.943398113.

Subproblem 1

x + 0.7 = 0.943398113 Simplifying x + 0.7 = 0.943398113 Reorder the terms: 0.7 + x = 0.943398113 Solving 0.7 + x = 0.943398113 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 = 0.943398113 + -0.7 Combine like terms: 0.7 + -0.7 = 0.0 0.0 + x = 0.943398113 + -0.7 x = 0.943398113 + -0.7 Combine like terms: 0.943398113 + -0.7 = 0.243398113 x = 0.243398113 Simplifying x = 0.243398113

Subproblem 2

x + 0.7 = -0.943398113 Simplifying x + 0.7 = -0.943398113 Reorder the terms: 0.7 + x = -0.943398113 Solving 0.7 + x = -0.943398113 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 = -0.943398113 + -0.7 Combine like terms: 0.7 + -0.7 = 0.0 0.0 + x = -0.943398113 + -0.7 x = -0.943398113 + -0.7 Combine like terms: -0.943398113 + -0.7 = -1.643398113 x = -1.643398113 Simplifying x = -1.643398113

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.243398113, -1.643398113}

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