5x^2+7x-5=

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


Simplifying
5x2 + 7x + -5 = 0

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

Solving
-5 + 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'.
-1 + 1.4x + x2 = 0

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + 1.4x + 1 + x2 = 0 + 1

Reorder the terms:
-1 + 1 + 1.4x + x2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 1.4x + x2 = 0 + 1
1.4x + x2 = 0 + 1

Combine like terms: 0 + 1 = 1
1.4x + x2 = 1

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 = 1 + 0.49

Reorder the terms:
0.49 + 1.4x + x2 = 1 + 0.49

Combine like terms: 1 + 0.49 = 1.49
0.49 + 1.4x + x2 = 1.49

Factor a perfect square on the left side:
(x + 0.7)(x + 0.7) = 1.49

Calculate the square root of the right side: 1.220655562

Break this problem into two subproblems by setting 
(x + 0.7) equal to 1.220655562 and -1.220655562.

Subproblem 1

x + 0.7 = 1.220655562 Simplifying x + 0.7 = 1.220655562 Reorder the terms: 0.7 + x = 1.220655562 Solving 0.7 + x = 1.220655562 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 = 1.220655562 + -0.7 Combine like terms: 0.7 + -0.7 = 0.0 0.0 + x = 1.220655562 + -0.7 x = 1.220655562 + -0.7 Combine like terms: 1.220655562 + -0.7 = 0.520655562 x = 0.520655562 Simplifying x = 0.520655562

Subproblem 2

x + 0.7 = -1.220655562 Simplifying x + 0.7 = -1.220655562 Reorder the terms: 0.7 + x = -1.220655562 Solving 0.7 + x = -1.220655562 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 = -1.220655562 + -0.7 Combine like terms: 0.7 + -0.7 = 0.0 0.0 + x = -1.220655562 + -0.7 x = -1.220655562 + -0.7 Combine like terms: -1.220655562 + -0.7 = -1.920655562 x = -1.920655562 Simplifying x = -1.920655562

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.520655562, -1.920655562}

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