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Simplifying -4x2 + 240x + 14400 = 18400 Reorder the terms: 14400 + 240x + -4x2 = 18400 Solving 14400 + 240x + -4x2 = 18400 Solving for variable 'x'. Reorder the terms: 14400 + -18400 + 240x + -4x2 = 18400 + -18400 Combine like terms: 14400 + -18400 = -4000 -4000 + 240x + -4x2 = 18400 + -18400 Combine like terms: 18400 + -18400 = 0 -4000 + 240x + -4x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-1000 + 60x + -1x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-1000 + 60x + -1x2)' equal to zero and attempt to solve: Simplifying -1000 + 60x + -1x2 = 0 Solving -1000 + 60x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 1000 + -60x + x2 = 0 Move the constant term to the right: Add '-1000' to each side of the equation. 1000 + -60x + -1000 + x2 = 0 + -1000 Reorder the terms: 1000 + -1000 + -60x + x2 = 0 + -1000 Combine like terms: 1000 + -1000 = 0 0 + -60x + x2 = 0 + -1000 -60x + x2 = 0 + -1000 Combine like terms: 0 + -1000 = -1000 -60x + x2 = -1000 The x term is -60x. Take half its coefficient (-30). Square it (900) and add it to both sides. Add '900' to each side of the equation. -60x + 900 + x2 = -1000 + 900 Reorder the terms: 900 + -60x + x2 = -1000 + 900 Combine like terms: -1000 + 900 = -100 900 + -60x + x2 = -100 Factor a perfect square on the left side: (x + -30)(x + -30) = -100 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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