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Simplifying 0 = 5x2 + -20x + 80 Reorder the terms: 0 = 80 + -20x + 5x2 Solving 0 = 80 + -20x + 5x2 Solving for variable 'x'. Combine like terms: 0 + -80 = -80 -80 + 20x + -5x2 = 80 + -20x + 5x2 + -80 + 20x + -5x2 Reorder the terms: -80 + 20x + -5x2 = 80 + -80 + -20x + 20x + 5x2 + -5x2 Combine like terms: 80 + -80 = 0 -80 + 20x + -5x2 = 0 + -20x + 20x + 5x2 + -5x2 -80 + 20x + -5x2 = -20x + 20x + 5x2 + -5x2 Combine like terms: -20x + 20x = 0 -80 + 20x + -5x2 = 0 + 5x2 + -5x2 -80 + 20x + -5x2 = 5x2 + -5x2 Combine like terms: 5x2 + -5x2 = 0 -80 + 20x + -5x2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(-16 + 4x + -1x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-16 + 4x + -1x2)' equal to zero and attempt to solve: Simplifying -16 + 4x + -1x2 = 0 Solving -16 + 4x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 16 + -4x + x2 = 0 Move the constant term to the right: Add '-16' to each side of the equation. 16 + -4x + -16 + x2 = 0 + -16 Reorder the terms: 16 + -16 + -4x + x2 = 0 + -16 Combine like terms: 16 + -16 = 0 0 + -4x + x2 = 0 + -16 -4x + x2 = 0 + -16 Combine like terms: 0 + -16 = -16 -4x + x2 = -16 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = -16 + 4 Reorder the terms: 4 + -4x + x2 = -16 + 4 Combine like terms: -16 + 4 = -12 4 + -4x + x2 = -12 Factor a perfect square on the left side: (x + -2)(x + -2) = -12 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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