2x(5-2x)=42

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Solution for 2x(5-2x)=42 equation: 


Simplifying
2x(5 + -2x) = 42
(5 * 2x + -2x * 2x) = 42
(10x + -4x2) = 42

Solving
10x + -4x2 = 42

Solving for variable 'x'.

Reorder the terms:
-42 + 10x + -4x2 = 42 + -42

Combine like terms: 42 + -42 = 0
-42 + 10x + -4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-21 + 5x + -2x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-21 + 5x + -2x2)' equal to zero and attempt to solve:

Simplifying
-21 + 5x + -2x2 = 0

Solving
-21 + 5x + -2x2 = 0

Begin completing the square.  Divide all terms by
-2 the coefficient of the squared term: 

Divide each side by '-2'.
10.5 + -2.5x + x2 = 0

Move the constant term to the right:

Add '-10.5' to each side of the equation.
10.5 + -2.5x + -10.5 + x2 = 0 + -10.5

Reorder the terms:
10.5 + -10.5 + -2.5x + x2 = 0 + -10.5

Combine like terms: 10.5 + -10.5 = 0.0
0.0 + -2.5x + x2 = 0 + -10.5
-2.5x + x2 = 0 + -10.5

Combine like terms: 0 + -10.5 = -10.5
-2.5x + x2 = -10.5

The x term is -2.5x.  Take half its coefficient (-1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
-2.5x + 1.5625 + x2 = -10.5 + 1.5625

Reorder the terms:
1.5625 + -2.5x + x2 = -10.5 + 1.5625

Combine like terms: -10.5 + 1.5625 = -8.9375
1.5625 + -2.5x + x2 = -8.9375

Factor a perfect square on the left side:
(x + -1.25)(x + -1.25) = -8.9375

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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