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Simplifying 30000 + 1700x + -20x(20x) = 51000 Remove parenthesis around (20x) 30000 + 1700x + -20x * 20x = 51000 Reorder the terms for easier multiplication: 30000 + 1700x + -20 * 20x * x = 51000 Multiply -20 * 20 30000 + 1700x + -400x * x = 51000 Multiply x * x 30000 + 1700x + -400x2 = 51000 Solving 30000 + 1700x + -400x2 = 51000 Solving for variable 'x'. Reorder the terms: 30000 + -51000 + 1700x + -400x2 = 51000 + -51000 Combine like terms: 30000 + -51000 = -21000 -21000 + 1700x + -400x2 = 51000 + -51000 Combine like terms: 51000 + -51000 = 0 -21000 + 1700x + -400x2 = 0 Factor out the Greatest Common Factor (GCF), '100'. 100(-210 + 17x + -4x2) = 0 Ignore the factor 100.Subproblem 1
Set the factor '(-210 + 17x + -4x2)' equal to zero and attempt to solve: Simplifying -210 + 17x + -4x2 = 0 Solving -210 + 17x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. 52.5 + -4.25x + x2 = 0 Move the constant term to the right: Add '-52.5' to each side of the equation. 52.5 + -4.25x + -52.5 + x2 = 0 + -52.5 Reorder the terms: 52.5 + -52.5 + -4.25x + x2 = 0 + -52.5 Combine like terms: 52.5 + -52.5 = 0.0 0.0 + -4.25x + x2 = 0 + -52.5 -4.25x + x2 = 0 + -52.5 Combine like terms: 0 + -52.5 = -52.5 -4.25x + x2 = -52.5 The x term is -4.25x. Take half its coefficient (-2.125). Square it (4.515625) and add it to both sides. Add '4.515625' to each side of the equation. -4.25x + 4.515625 + x2 = -52.5 + 4.515625 Reorder the terms: 4.515625 + -4.25x + x2 = -52.5 + 4.515625 Combine like terms: -52.5 + 4.515625 = -47.984375 4.515625 + -4.25x + x2 = -47.984375 Factor a perfect square on the left side: (x + -2.125)(x + -2.125) = -47.984375 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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