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Simplifying 140 = 5x + -4x(5x + -5) Reorder the terms: 140 = 5x + -4x(-5 + 5x) 140 = 5x + (-5 * -4x + 5x * -4x) 140 = 5x + (20x + -20x2) Combine like terms: 5x + 20x = 25x 140 = 25x + -20x2 Solving 140 = 25x + -20x2 Solving for variable 'x'. Reorder the terms: 140 + -25x + 20x2 = 25x + -25x + -20x2 + 20x2 Combine like terms: 25x + -25x = 0 140 + -25x + 20x2 = 0 + -20x2 + 20x2 140 + -25x + 20x2 = -20x2 + 20x2 Combine like terms: -20x2 + 20x2 = 0 140 + -25x + 20x2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(28 + -5x + 4x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(28 + -5x + 4x2)' equal to zero and attempt to solve: Simplifying 28 + -5x + 4x2 = 0 Solving 28 + -5x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 7 + -1.25x + x2 = 0 Move the constant term to the right: Add '-7' to each side of the equation. 7 + -1.25x + -7 + x2 = 0 + -7 Reorder the terms: 7 + -7 + -1.25x + x2 = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1.25x + x2 = 0 + -7 -1.25x + x2 = 0 + -7 Combine like terms: 0 + -7 = -7 -1.25x + x2 = -7 The x term is -1.25x. Take half its coefficient (-0.625). Square it (0.390625) and add it to both sides. Add '0.390625' to each side of the equation. -1.25x + 0.390625 + x2 = -7 + 0.390625 Reorder the terms: 0.390625 + -1.25x + x2 = -7 + 0.390625 Combine like terms: -7 + 0.390625 = -6.609375 0.390625 + -1.25x + x2 = -6.609375 Factor a perfect square on the left side: (x + -0.625)(x + -0.625) = -6.609375 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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