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Simplifying 400 = -4x2 + 80x + -150 Reorder the terms: 400 = -150 + 80x + -4x2 Solving 400 = -150 + 80x + -4x2 Solving for variable 'x'. Combine like terms: 400 + 150 = 550 550 + -80x + 4x2 = -150 + 80x + -4x2 + 150 + -80x + 4x2 Reorder the terms: 550 + -80x + 4x2 = -150 + 150 + 80x + -80x + -4x2 + 4x2 Combine like terms: -150 + 150 = 0 550 + -80x + 4x2 = 0 + 80x + -80x + -4x2 + 4x2 550 + -80x + 4x2 = 80x + -80x + -4x2 + 4x2 Combine like terms: 80x + -80x = 0 550 + -80x + 4x2 = 0 + -4x2 + 4x2 550 + -80x + 4x2 = -4x2 + 4x2 Combine like terms: -4x2 + 4x2 = 0 550 + -80x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(275 + -40x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(275 + -40x + 2x2)' equal to zero and attempt to solve: Simplifying 275 + -40x + 2x2 = 0 Solving 275 + -40x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 137.5 + -20x + x2 = 0 Move the constant term to the right: Add '-137.5' to each side of the equation. 137.5 + -20x + -137.5 + x2 = 0 + -137.5 Reorder the terms: 137.5 + -137.5 + -20x + x2 = 0 + -137.5 Combine like terms: 137.5 + -137.5 = 0.0 0.0 + -20x + x2 = 0 + -137.5 -20x + x2 = 0 + -137.5 Combine like terms: 0 + -137.5 = -137.5 -20x + x2 = -137.5 The x term is -20x. Take half its coefficient (-10). Square it (100) and add it to both sides. Add '100' to each side of the equation. -20x + 100 + x2 = -137.5 + 100 Reorder the terms: 100 + -20x + x2 = -137.5 + 100 Combine like terms: -137.5 + 100 = -37.5 100 + -20x + x2 = -37.5 Factor a perfect square on the left side: (x + -10)(x + -10) = -37.5 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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