3x-2x(5x+3)=14-2x

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Solution for 3x-2x(5x+3)=14-2x equation:


Simplifying
3x + -2x(5x + 3) = 14 + -2x

Reorder the terms:
3x + -2x(3 + 5x) = 14 + -2x
3x + (3 * -2x + 5x * -2x) = 14 + -2x
3x + (-6x + -10x2) = 14 + -2x

Combine like terms: 3x + -6x = -3x
-3x + -10x2 = 14 + -2x

Solving
-3x + -10x2 = 14 + -2x

Solving for variable 'x'.

Reorder the terms:
-14 + -3x + 2x + -10x2 = 14 + -2x + -14 + 2x

Combine like terms: -3x + 2x = -1x
-14 + -1x + -10x2 = 14 + -2x + -14 + 2x

Reorder the terms:
-14 + -1x + -10x2 = 14 + -14 + -2x + 2x

Combine like terms: 14 + -14 = 0
-14 + -1x + -10x2 = 0 + -2x + 2x
-14 + -1x + -10x2 = -2x + 2x

Combine like terms: -2x + 2x = 0
-14 + -1x + -10x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(14 + x + 10x2) = 0

Ignore the factor -1.

Subproblem 1

Set the factor '(14 + x + 10x2)' equal to zero and attempt to solve: Simplifying 14 + x + 10x2 = 0 Solving 14 + x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. 1.4 + 0.1x + x2 = 0.0 Move the constant term to the right: Add '-1.4' to each side of the equation. 1.4 + 0.1x + -1.4 + x2 = 0.0 + -1.4 Reorder the terms: 1.4 + -1.4 + 0.1x + x2 = 0.0 + -1.4 Combine like terms: 1.4 + -1.4 = 0.0 0.0 + 0.1x + x2 = 0.0 + -1.4 0.1x + x2 = 0.0 + -1.4 Combine like terms: 0.0 + -1.4 = -1.4 0.1x + x2 = -1.4 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.1x + 0.25 + x2 = -1.4 + 0.25 Reorder the terms: 0.25 + 0.1x + x2 = -1.4 + 0.25 Combine like terms: -1.4 + 0.25 = -1.15 0.25 + 0.1x + x2 = -1.15 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = -1.15 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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