10x^2-24x=-32

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Solution for 10x^2-24x=-32 equation: 


Simplifying
10x2 + -24x = -32

Reorder the terms:
-24x + 10x2 = -32

Solving
-24x + 10x2 = -32

Solving for variable 'x'.

Reorder the terms:
32 + -24x + 10x2 = -32 + 32

Combine like terms: -32 + 32 = 0
32 + -24x + 10x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(16 + -12x + 5x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(16 + -12x + 5x2)' equal to zero and attempt to solve:

Simplifying
16 + -12x + 5x2 = 0

Solving
16 + -12x + 5x2 = 0

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

Divide each side by '5'.
3.2 + -2.4x + x2 = 0

Move the constant term to the right:

Add '-3.2' to each side of the equation.
3.2 + -2.4x + -3.2 + x2 = 0 + -3.2

Reorder the terms:
3.2 + -3.2 + -2.4x + x2 = 0 + -3.2

Combine like terms: 3.2 + -3.2 = 0.0
0.0 + -2.4x + x2 = 0 + -3.2
-2.4x + x2 = 0 + -3.2

Combine like terms: 0 + -3.2 = -3.2
-2.4x + x2 = -3.2

The x term is -2.4x.  Take half its coefficient (-1.2).
Square it (1.44) and add it to both sides.

Add '1.44' to each side of the equation.
-2.4x + 1.44 + x2 = -3.2 + 1.44

Reorder the terms:
1.44 + -2.4x + x2 = -3.2 + 1.44

Combine like terms: -3.2 + 1.44 = -1.76
1.44 + -2.4x + x2 = -1.76

Factor a perfect square on the left side:
(x + -1.2)(x + -1.2) = -1.76

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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