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Simplifying 0 = 5x2 + -15x + 20 Reorder the terms: 0 = 20 + -15x + 5x2 Solving 0 = 20 + -15x + 5x2 Solving for variable 'x'. Combine like terms: 0 + -20 = -20 -20 + 15x + -5x2 = 20 + -15x + 5x2 + -20 + 15x + -5x2 Reorder the terms: -20 + 15x + -5x2 = 20 + -20 + -15x + 15x + 5x2 + -5x2 Combine like terms: 20 + -20 = 0 -20 + 15x + -5x2 = 0 + -15x + 15x + 5x2 + -5x2 -20 + 15x + -5x2 = -15x + 15x + 5x2 + -5x2 Combine like terms: -15x + 15x = 0 -20 + 15x + -5x2 = 0 + 5x2 + -5x2 -20 + 15x + -5x2 = 5x2 + -5x2 Combine like terms: 5x2 + -5x2 = 0 -20 + 15x + -5x2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(-4 + 3x + -1x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-4 + 3x + -1x2)' equal to zero and attempt to solve: Simplifying -4 + 3x + -1x2 = 0 Solving -4 + 3x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 4 + -3x + x2 = 0 Move the constant term to the right: Add '-4' to each side of the equation. 4 + -3x + -4 + x2 = 0 + -4 Reorder the terms: 4 + -4 + -3x + x2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -3x + x2 = 0 + -4 -3x + x2 = 0 + -4 Combine like terms: 0 + -4 = -4 -3x + x2 = -4 The x term is -3x. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3x + 2.25 + x2 = -4 + 2.25 Reorder the terms: 2.25 + -3x + x2 = -4 + 2.25 Combine like terms: -4 + 2.25 = -1.75 2.25 + -3x + x2 = -1.75 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = -1.75 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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