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Simplifying (120 + -2x)(70 + 2x) = 15000 Multiply (120 + -2x) * (70 + 2x) (120(70 + 2x) + -2x * (70 + 2x)) = 15000 ((70 * 120 + 2x * 120) + -2x * (70 + 2x)) = 15000 ((8400 + 240x) + -2x * (70 + 2x)) = 15000 (8400 + 240x + (70 * -2x + 2x * -2x)) = 15000 (8400 + 240x + (-140x + -4x2)) = 15000 Combine like terms: 240x + -140x = 100x (8400 + 100x + -4x2) = 15000 Solving 8400 + 100x + -4x2 = 15000 Solving for variable 'x'. Reorder the terms: 8400 + -15000 + 100x + -4x2 = 15000 + -15000 Combine like terms: 8400 + -15000 = -6600 -6600 + 100x + -4x2 = 15000 + -15000 Combine like terms: 15000 + -15000 = 0 -6600 + 100x + -4x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-1650 + 25x + -1x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-1650 + 25x + -1x2)' equal to zero and attempt to solve: Simplifying -1650 + 25x + -1x2 = 0 Solving -1650 + 25x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 1650 + -25x + x2 = 0 Move the constant term to the right: Add '-1650' to each side of the equation. 1650 + -25x + -1650 + x2 = 0 + -1650 Reorder the terms: 1650 + -1650 + -25x + x2 = 0 + -1650 Combine like terms: 1650 + -1650 = 0 0 + -25x + x2 = 0 + -1650 -25x + x2 = 0 + -1650 Combine like terms: 0 + -1650 = -1650 -25x + x2 = -1650 The x term is -25x. Take half its coefficient (-12.5). Square it (156.25) and add it to both sides. Add '156.25' to each side of the equation. -25x + 156.25 + x2 = -1650 + 156.25 Reorder the terms: 156.25 + -25x + x2 = -1650 + 156.25 Combine like terms: -1650 + 156.25 = -1493.75 156.25 + -25x + x2 = -1493.75 Factor a perfect square on the left side: (x + -12.5)(x + -12.5) = -1493.75 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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