5x+2=x^2(4)-6-3x+18

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Solution for 5x+2=x^2(4)-6-3x+18 equation:


Simplifying
5x + 2 = x2(4) + -6 + -3x + 18

Reorder the terms:
2 + 5x = x2(4) + -6 + -3x + 18

Reorder the terms for easier multiplication:
2 + 5x = 4x2 + -6 + -3x + 18

Reorder the terms:
2 + 5x = -6 + 18 + -3x + 4x2

Combine like terms: -6 + 18 = 12
2 + 5x = 12 + -3x + 4x2

Solving
2 + 5x = 12 + -3x + 4x2

Solving for variable 'x'.

Reorder the terms:
2 + -12 + 5x + 3x + -4x2 = 12 + -3x + 4x2 + -12 + 3x + -4x2

Combine like terms: 2 + -12 = -10
-10 + 5x + 3x + -4x2 = 12 + -3x + 4x2 + -12 + 3x + -4x2

Combine like terms: 5x + 3x = 8x
-10 + 8x + -4x2 = 12 + -3x + 4x2 + -12 + 3x + -4x2

Reorder the terms:
-10 + 8x + -4x2 = 12 + -12 + -3x + 3x + 4x2 + -4x2

Combine like terms: 12 + -12 = 0
-10 + 8x + -4x2 = 0 + -3x + 3x + 4x2 + -4x2
-10 + 8x + -4x2 = -3x + 3x + 4x2 + -4x2

Combine like terms: -3x + 3x = 0
-10 + 8x + -4x2 = 0 + 4x2 + -4x2
-10 + 8x + -4x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
-10 + 8x + -4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-5 + 4x + -2x2) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(-5 + 4x + -2x2)' equal to zero and attempt to solve: Simplifying -5 + 4x + -2x2 = 0 Solving -5 + 4x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. 2.5 + -2x + x2 = 0 Move the constant term to the right: Add '-2.5' to each side of the equation. 2.5 + -2x + -2.5 + x2 = 0 + -2.5 Reorder the terms: 2.5 + -2.5 + -2x + x2 = 0 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + -2x + x2 = 0 + -2.5 -2x + x2 = 0 + -2.5 Combine like terms: 0 + -2.5 = -2.5 -2x + x2 = -2.5 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = -2.5 + 1 Reorder the terms: 1 + -2x + x2 = -2.5 + 1 Combine like terms: -2.5 + 1 = -1.5 1 + -2x + x2 = -1.5 Factor a perfect square on the left side: (x + -1)(x + -1) = -1.5 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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