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Simplifying 20x + -5x2 = 100 Solving 20x + -5x2 = 100 Solving for variable 'x'. Reorder the terms: -100 + 20x + -5x2 = 100 + -100 Combine like terms: 100 + -100 = 0 -100 + 20x + -5x2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(-20 + 4x + -1x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-20 + 4x + -1x2)' equal to zero and attempt to solve: Simplifying -20 + 4x + -1x2 = 0 Solving -20 + 4x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 20 + -4x + x2 = 0 Move the constant term to the right: Add '-20' to each side of the equation. 20 + -4x + -20 + x2 = 0 + -20 Reorder the terms: 20 + -20 + -4x + x2 = 0 + -20 Combine like terms: 20 + -20 = 0 0 + -4x + x2 = 0 + -20 -4x + x2 = 0 + -20 Combine like terms: 0 + -20 = -20 -4x + x2 = -20 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 = -20 + 4 Reorder the terms: 4 + -4x + x2 = -20 + 4 Combine like terms: -20 + 4 = -16 4 + -4x + x2 = -16 Factor a perfect square on the left side: (x + -2)(x + -2) = -16 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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