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Simplifying (5x2) + 20x = (20x2) + 80 Reorder the terms: 20x + (5x2) = (20x2) + 80 Reorder the terms: 20x + (5x2) = 80 + (20x2) Solving 20x + (5x2) = 80 + (20x2) Solving for variable 'x'. Reorder the terms: -80 + 20x + (5x2) + (-20x2) = 80 + (20x2) + -80 + (-20x2) Combine like terms: (5x2) + (-20x2) = -15x2 -80 + 20x + -15x2 = 80 + (20x2) + -80 + (-20x2) Reorder the terms: -80 + 20x + -15x2 = 80 + -80 + (20x2) + (-20x2) Combine like terms: 80 + -80 = 0 -80 + 20x + -15x2 = 0 + (20x2) + (-20x2) -80 + 20x + -15x2 = (20x2) + (-20x2) Combine like terms: (20x2) + (-20x2) = 0 -80 + 20x + -15x2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(-16 + 4x + -3x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-16 + 4x + -3x2)' equal to zero and attempt to solve: Simplifying -16 + 4x + -3x2 = 0 Solving -16 + 4x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. 5.333333333 + -1.333333333x + x2 = 0 Move the constant term to the right: Add '-5.333333333' to each side of the equation. 5.333333333 + -1.333333333x + -5.333333333 + x2 = 0 + -5.333333333 Reorder the terms: 5.333333333 + -5.333333333 + -1.333333333x + x2 = 0 + -5.333333333 Combine like terms: 5.333333333 + -5.333333333 = 0.000000000 0.000000000 + -1.333333333x + x2 = 0 + -5.333333333 -1.333333333x + x2 = 0 + -5.333333333 Combine like terms: 0 + -5.333333333 = -5.333333333 -1.333333333x + x2 = -5.333333333 The x term is -1.333333333x. Take half its coefficient (-0.6666666665). Square it (0.4444444442) and add it to both sides. Add '0.4444444442' to each side of the equation. -1.333333333x + 0.4444444442 + x2 = -5.333333333 + 0.4444444442 Reorder the terms: 0.4444444442 + -1.333333333x + x2 = -5.333333333 + 0.4444444442 Combine like terms: -5.333333333 + 0.4444444442 = -4.8888888888 0.4444444442 + -1.333333333x + x2 = -4.8888888888 Factor a perfect square on the left side: (x + -0.6666666665)(x + -0.6666666665) = -4.8888888888 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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