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Simplifying 15 = -0.056x2 + 0.422x + 33.935 Reorder the terms: 15 = 33.935 + 0.422x + -0.056x2 Solving 15 = 33.935 + 0.422x + -0.056x2 Solving for variable 'x'. Combine like terms: 15 + -33.935 = -18.935 -18.935 + -0.422x + 0.056x2 = 33.935 + 0.422x + -0.056x2 + -33.935 + -0.422x + 0.056x2 Reorder the terms: -18.935 + -0.422x + 0.056x2 = 33.935 + -33.935 + 0.422x + -0.422x + -0.056x2 + 0.056x2 Combine like terms: 33.935 + -33.935 = 0.000 -18.935 + -0.422x + 0.056x2 = 0.000 + 0.422x + -0.422x + -0.056x2 + 0.056x2 -18.935 + -0.422x + 0.056x2 = 0.422x + -0.422x + -0.056x2 + 0.056x2 Combine like terms: 0.422x + -0.422x = 0.000 -18.935 + -0.422x + 0.056x2 = 0.000 + -0.056x2 + 0.056x2 -18.935 + -0.422x + 0.056x2 = -0.056x2 + 0.056x2 Combine like terms: -0.056x2 + 0.056x2 = 0.000 -18.935 + -0.422x + 0.056x2 = 0.000 Begin completing the square. Divide all terms by 0.056 the coefficient of the squared term: Divide each side by '0.056'. -338.125 + -7.535714286x + x2 = 0 Move the constant term to the right: Add '338.125' to each side of the equation. -338.125 + -7.535714286x + 338.125 + x2 = 0 + 338.125 Reorder the terms: -338.125 + 338.125 + -7.535714286x + x2 = 0 + 338.125 Combine like terms: -338.125 + 338.125 = 0.000 0.000 + -7.535714286x + x2 = 0 + 338.125 -7.535714286x + x2 = 0 + 338.125 Combine like terms: 0 + 338.125 = 338.125 -7.535714286x + x2 = 338.125 The x term is -7.535714286x. Take half its coefficient (-3.767857143). Square it (14.19674745) and add it to both sides. Add '14.19674745' to each side of the equation. -7.535714286x + 14.19674745 + x2 = 338.125 + 14.19674745 Reorder the terms: 14.19674745 + -7.535714286x + x2 = 338.125 + 14.19674745 Combine like terms: 338.125 + 14.19674745 = 352.32174745 14.19674745 + -7.535714286x + x2 = 352.32174745 Factor a perfect square on the left side: (x + -3.767857143)(x + -3.767857143) = 352.32174745 Calculate the square root of the right side: 18.770235679 Break this problem into two subproblems by setting (x + -3.767857143) equal to 18.770235679 and -18.770235679.Subproblem 1
x + -3.767857143 = 18.770235679 Simplifying x + -3.767857143 = 18.770235679 Reorder the terms: -3.767857143 + x = 18.770235679 Solving -3.767857143 + x = 18.770235679 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.767857143' to each side of the equation. -3.767857143 + 3.767857143 + x = 18.770235679 + 3.767857143 Combine like terms: -3.767857143 + 3.767857143 = 0.000000000 0.000000000 + x = 18.770235679 + 3.767857143 x = 18.770235679 + 3.767857143 Combine like terms: 18.770235679 + 3.767857143 = 22.538092822 x = 22.538092822 Simplifying x = 22.538092822Subproblem 2
x + -3.767857143 = -18.770235679 Simplifying x + -3.767857143 = -18.770235679 Reorder the terms: -3.767857143 + x = -18.770235679 Solving -3.767857143 + x = -18.770235679 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.767857143' to each side of the equation. -3.767857143 + 3.767857143 + x = -18.770235679 + 3.767857143 Combine like terms: -3.767857143 + 3.767857143 = 0.000000000 0.000000000 + x = -18.770235679 + 3.767857143 x = -18.770235679 + 3.767857143 Combine like terms: -18.770235679 + 3.767857143 = -15.002378536 x = -15.002378536 Simplifying x = -15.002378536Solution
The solution to the problem is based on the solutions from the subproblems. x = {22.538092822, -15.002378536}
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