25x^2+80x+62=0

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Solution for 25x^2+80x+62=0 equation:


Simplifying
25x2 + 80x + 62 = 0

Reorder the terms:
62 + 80x + 25x2 = 0

Solving
62 + 80x + 25x2 = 0

Solving for variable 'x'.

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

Divide each side by '25'.
2.48 + 3.2x + x2 = 0

Move the constant term to the right:

Add '-2.48' to each side of the equation.
2.48 + 3.2x + -2.48 + x2 = 0 + -2.48

Reorder the terms:
2.48 + -2.48 + 3.2x + x2 = 0 + -2.48

Combine like terms: 2.48 + -2.48 = 0.00
0.00 + 3.2x + x2 = 0 + -2.48
3.2x + x2 = 0 + -2.48

Combine like terms: 0 + -2.48 = -2.48
3.2x + x2 = -2.48

The x term is 3.2x.  Take half its coefficient (1.6).
Square it (2.56) and add it to both sides.

Add '2.56' to each side of the equation.
3.2x + 2.56 + x2 = -2.48 + 2.56

Reorder the terms:
2.56 + 3.2x + x2 = -2.48 + 2.56

Combine like terms: -2.48 + 2.56 = 0.08
2.56 + 3.2x + x2 = 0.08

Factor a perfect square on the left side:
(x + 1.6)(x + 1.6) = 0.08

Calculate the square root of the right side: 0.282842712

Break this problem into two subproblems by setting 
(x + 1.6) equal to 0.282842712 and -0.282842712.

Subproblem 1

x + 1.6 = 0.282842712 Simplifying x + 1.6 = 0.282842712 Reorder the terms: 1.6 + x = 0.282842712 Solving 1.6 + x = 0.282842712 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.6' to each side of the equation. 1.6 + -1.6 + x = 0.282842712 + -1.6 Combine like terms: 1.6 + -1.6 = 0.0 0.0 + x = 0.282842712 + -1.6 x = 0.282842712 + -1.6 Combine like terms: 0.282842712 + -1.6 = -1.317157288 x = -1.317157288 Simplifying x = -1.317157288

Subproblem 2

x + 1.6 = -0.282842712 Simplifying x + 1.6 = -0.282842712 Reorder the terms: 1.6 + x = -0.282842712 Solving 1.6 + x = -0.282842712 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.6' to each side of the equation. 1.6 + -1.6 + x = -0.282842712 + -1.6 Combine like terms: 1.6 + -1.6 = 0.0 0.0 + x = -0.282842712 + -1.6 x = -0.282842712 + -1.6 Combine like terms: -0.282842712 + -1.6 = -1.882842712 x = -1.882842712 Simplifying x = -1.882842712

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-1.317157288, -1.882842712}

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