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Simplifying 500x + 27500 + -14x2 = 0 Reorder the terms: 27500 + 500x + -14x2 = 0 Solving 27500 + 500x + -14x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(13750 + 250x + -7x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(13750 + 250x + -7x2)' equal to zero and attempt to solve: Simplifying 13750 + 250x + -7x2 = 0 Solving 13750 + 250x + -7x2 = 0 Begin completing the square. Divide all terms by -7 the coefficient of the squared term: Divide each side by '-7'. -1964.285714 + -35.71428571x + x2 = 0 Move the constant term to the right: Add '1964.285714' to each side of the equation. -1964.285714 + -35.71428571x + 1964.285714 + x2 = 0 + 1964.285714 Reorder the terms: -1964.285714 + 1964.285714 + -35.71428571x + x2 = 0 + 1964.285714 Combine like terms: -1964.285714 + 1964.285714 = 0.000000 0.000000 + -35.71428571x + x2 = 0 + 1964.285714 -35.71428571x + x2 = 0 + 1964.285714 Combine like terms: 0 + 1964.285714 = 1964.285714 -35.71428571x + x2 = 1964.285714 The x term is -35.71428571x. Take half its coefficient (-17.85714286). Square it (318.8775511) and add it to both sides. Add '318.8775511' to each side of the equation. -35.71428571x + 318.8775511 + x2 = 1964.285714 + 318.8775511 Reorder the terms: 318.8775511 + -35.71428571x + x2 = 1964.285714 + 318.8775511 Combine like terms: 1964.285714 + 318.8775511 = 2283.1632651 318.8775511 + -35.71428571x + x2 = 2283.1632651 Factor a perfect square on the left side: (x + -17.85714286)(x + -17.85714286) = 2283.1632651 Calculate the square root of the right side: 47.782457713 Break this problem into two subproblems by setting (x + -17.85714286) equal to 47.782457713 and -47.782457713.Subproblem 1
x + -17.85714286 = 47.782457713 Simplifying x + -17.85714286 = 47.782457713 Reorder the terms: -17.85714286 + x = 47.782457713 Solving -17.85714286 + x = 47.782457713 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '17.85714286' to each side of the equation. -17.85714286 + 17.85714286 + x = 47.782457713 + 17.85714286 Combine like terms: -17.85714286 + 17.85714286 = 0.00000000 0.00000000 + x = 47.782457713 + 17.85714286 x = 47.782457713 + 17.85714286 Combine like terms: 47.782457713 + 17.85714286 = 65.639600573 x = 65.639600573 Simplifying x = 65.639600573Subproblem 2
x + -17.85714286 = -47.782457713 Simplifying x + -17.85714286 = -47.782457713 Reorder the terms: -17.85714286 + x = -47.782457713 Solving -17.85714286 + x = -47.782457713 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '17.85714286' to each side of the equation. -17.85714286 + 17.85714286 + x = -47.782457713 + 17.85714286 Combine like terms: -17.85714286 + 17.85714286 = 0.00000000 0.00000000 + x = -47.782457713 + 17.85714286 x = -47.782457713 + 17.85714286 Combine like terms: -47.782457713 + 17.85714286 = -29.925314853 x = -29.925314853 Simplifying x = -29.925314853Solution
The solution to the problem is based on the solutions from the subproblems. x = {65.639600573, -29.925314853}Solution
x = {65.639600573, -29.925314853}
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