5x^2+8x-3=0

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Solution for 5x^2+8x-3=0 equation:


Simplifying
5x2 + 8x + -3 = 0

Reorder the terms:
-3 + 8x + 5x2 = 0

Solving
-3 + 8x + 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'.
-0.6 + 1.6x + x2 = 0

Move the constant term to the right:

Add '0.6' to each side of the equation.
-0.6 + 1.6x + 0.6 + x2 = 0 + 0.6

Reorder the terms:
-0.6 + 0.6 + 1.6x + x2 = 0 + 0.6

Combine like terms: -0.6 + 0.6 = 0.0
0.0 + 1.6x + x2 = 0 + 0.6
1.6x + x2 = 0 + 0.6

Combine like terms: 0 + 0.6 = 0.6
1.6x + x2 = 0.6

The x term is 1.6x.  Take half its coefficient (0.8).
Square it (0.64) and add it to both sides.

Add '0.64' to each side of the equation.
1.6x + 0.64 + x2 = 0.6 + 0.64

Reorder the terms:
0.64 + 1.6x + x2 = 0.6 + 0.64

Combine like terms: 0.6 + 0.64 = 1.24
0.64 + 1.6x + x2 = 1.24

Factor a perfect square on the left side:
(x + 0.8)(x + 0.8) = 1.24

Calculate the square root of the right side: 1.113552873

Break this problem into two subproblems by setting 
(x + 0.8) equal to 1.113552873 and -1.113552873.

Subproblem 1

x + 0.8 = 1.113552873 Simplifying x + 0.8 = 1.113552873 Reorder the terms: 0.8 + x = 1.113552873 Solving 0.8 + x = 1.113552873 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8' to each side of the equation. 0.8 + -0.8 + x = 1.113552873 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + x = 1.113552873 + -0.8 x = 1.113552873 + -0.8 Combine like terms: 1.113552873 + -0.8 = 0.313552873 x = 0.313552873 Simplifying x = 0.313552873

Subproblem 2

x + 0.8 = -1.113552873 Simplifying x + 0.8 = -1.113552873 Reorder the terms: 0.8 + x = -1.113552873 Solving 0.8 + x = -1.113552873 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8' to each side of the equation. 0.8 + -0.8 + x = -1.113552873 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + x = -1.113552873 + -0.8 x = -1.113552873 + -0.8 Combine like terms: -1.113552873 + -0.8 = -1.913552873 x = -1.913552873 Simplifying x = -1.913552873

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.313552873, -1.913552873}

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