-62x^2-69x+28=0

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Solution for -62x^2-69x+28=0 equation:


Simplifying
-62x2 + -69x + 28 = 0

Reorder the terms:
28 + -69x + -62x2 = 0

Solving
28 + -69x + -62x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-62 the coefficient of the squared term: 

Divide each side by '-62'.
-0.4516129032 + 1.112903226x + x2 = 0

Move the constant term to the right:

Add '0.4516129032' to each side of the equation.
-0.4516129032 + 1.112903226x + 0.4516129032 + x2 = 0 + 0.4516129032

Reorder the terms:
-0.4516129032 + 0.4516129032 + 1.112903226x + x2 = 0 + 0.4516129032

Combine like terms: -0.4516129032 + 0.4516129032 = 0.0000000000
0.0000000000 + 1.112903226x + x2 = 0 + 0.4516129032
1.112903226x + x2 = 0 + 0.4516129032

Combine like terms: 0 + 0.4516129032 = 0.4516129032
1.112903226x + x2 = 0.4516129032

The x term is 1.112903226x.  Take half its coefficient (0.556451613).
Square it (0.3096383976) and add it to both sides.

Add '0.3096383976' to each side of the equation.
1.112903226x + 0.3096383976 + x2 = 0.4516129032 + 0.3096383976

Reorder the terms:
0.3096383976 + 1.112903226x + x2 = 0.4516129032 + 0.3096383976

Combine like terms: 0.4516129032 + 0.3096383976 = 0.7612513008
0.3096383976 + 1.112903226x + x2 = 0.7612513008

Factor a perfect square on the left side:
(x + 0.556451613)(x + 0.556451613) = 0.7612513008

Calculate the square root of the right side: 0.872497164

Break this problem into two subproblems by setting 
(x + 0.556451613) equal to 0.872497164 and -0.872497164.

Subproblem 1

x + 0.556451613 = 0.872497164 Simplifying x + 0.556451613 = 0.872497164 Reorder the terms: 0.556451613 + x = 0.872497164 Solving 0.556451613 + x = 0.872497164 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.556451613' to each side of the equation. 0.556451613 + -0.556451613 + x = 0.872497164 + -0.556451613 Combine like terms: 0.556451613 + -0.556451613 = 0.000000000 0.000000000 + x = 0.872497164 + -0.556451613 x = 0.872497164 + -0.556451613 Combine like terms: 0.872497164 + -0.556451613 = 0.316045551 x = 0.316045551 Simplifying x = 0.316045551

Subproblem 2

x + 0.556451613 = -0.872497164 Simplifying x + 0.556451613 = -0.872497164 Reorder the terms: 0.556451613 + x = -0.872497164 Solving 0.556451613 + x = -0.872497164 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.556451613' to each side of the equation. 0.556451613 + -0.556451613 + x = -0.872497164 + -0.556451613 Combine like terms: 0.556451613 + -0.556451613 = 0.000000000 0.000000000 + x = -0.872497164 + -0.556451613 x = -0.872497164 + -0.556451613 Combine like terms: -0.872497164 + -0.556451613 = -1.428948777 x = -1.428948777 Simplifying x = -1.428948777

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.316045551, -1.428948777}

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