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Simplifying 4.9x2 + -93.3x + -125 = 0 Reorder the terms: -125 + -93.3x + 4.9x2 = 0 Solving -125 + -93.3x + 4.9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4.9 the coefficient of the squared term: Divide each side by '4.9'. -25.51020408 + -19.04081633x + x2 = 0 Move the constant term to the right: Add '25.51020408' to each side of the equation. -25.51020408 + -19.04081633x + 25.51020408 + x2 = 0 + 25.51020408 Reorder the terms: -25.51020408 + 25.51020408 + -19.04081633x + x2 = 0 + 25.51020408 Combine like terms: -25.51020408 + 25.51020408 = 0.00000000 0.00000000 + -19.04081633x + x2 = 0 + 25.51020408 -19.04081633x + x2 = 0 + 25.51020408 Combine like terms: 0 + 25.51020408 = 25.51020408 -19.04081633x + x2 = 25.51020408 The x term is -19.04081633x. Take half its coefficient (-9.520408165). Square it (90.63817163) and add it to both sides. Add '90.63817163' to each side of the equation. -19.04081633x + 90.63817163 + x2 = 25.51020408 + 90.63817163 Reorder the terms: 90.63817163 + -19.04081633x + x2 = 25.51020408 + 90.63817163 Combine like terms: 25.51020408 + 90.63817163 = 116.14837571 90.63817163 + -19.04081633x + x2 = 116.14837571 Factor a perfect square on the left side: (x + -9.520408165)(x + -9.520408165) = 116.14837571 Calculate the square root of the right side: 10.777215582 Break this problem into two subproblems by setting (x + -9.520408165) equal to 10.777215582 and -10.777215582.Subproblem 1
x + -9.520408165 = 10.777215582 Simplifying x + -9.520408165 = 10.777215582 Reorder the terms: -9.520408165 + x = 10.777215582 Solving -9.520408165 + x = 10.777215582 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.520408165' to each side of the equation. -9.520408165 + 9.520408165 + x = 10.777215582 + 9.520408165 Combine like terms: -9.520408165 + 9.520408165 = 0.000000000 0.000000000 + x = 10.777215582 + 9.520408165 x = 10.777215582 + 9.520408165 Combine like terms: 10.777215582 + 9.520408165 = 20.297623747 x = 20.297623747 Simplifying x = 20.297623747Subproblem 2
x + -9.520408165 = -10.777215582 Simplifying x + -9.520408165 = -10.777215582 Reorder the terms: -9.520408165 + x = -10.777215582 Solving -9.520408165 + x = -10.777215582 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.520408165' to each side of the equation. -9.520408165 + 9.520408165 + x = -10.777215582 + 9.520408165 Combine like terms: -9.520408165 + 9.520408165 = 0.000000000 0.000000000 + x = -10.777215582 + 9.520408165 x = -10.777215582 + 9.520408165 Combine like terms: -10.777215582 + 9.520408165 = -1.256807417 x = -1.256807417 Simplifying x = -1.256807417Solution
The solution to the problem is based on the solutions from the subproblems. x = {20.297623747, -1.256807417}
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