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Simplifying (-4.9x2) + -22x + 108 = 0 Reorder the terms: 108 + -22x + (-4.9x2) = 0 Solving 108 + -22x + (-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'. -22.04081633 + 4.489795918x + x2 = 0 Move the constant term to the right: Add '22.04081633' to each side of the equation. -22.04081633 + 4.489795918x + 22.04081633 + x2 = 0 + 22.04081633 Reorder the terms: -22.04081633 + 22.04081633 + 4.489795918x + x2 = 0 + 22.04081633 Combine like terms: -22.04081633 + 22.04081633 = 0.00000000 0.00000000 + 4.489795918x + x2 = 0 + 22.04081633 4.489795918x + x2 = 0 + 22.04081633 Combine like terms: 0 + 22.04081633 = 22.04081633 4.489795918x + x2 = 22.04081633 The x term is 4.489795918x. Take half its coefficient (2.244897959). Square it (5.039566846) and add it to both sides. Add '5.039566846' to each side of the equation. 4.489795918x + 5.039566846 + x2 = 22.04081633 + 5.039566846 Reorder the terms: 5.039566846 + 4.489795918x + x2 = 22.04081633 + 5.039566846 Combine like terms: 22.04081633 + 5.039566846 = 27.080383176 5.039566846 + 4.489795918x + x2 = 27.080383176 Factor a perfect square on the left side: ((x) + 2.244897959)((x) + 2.244897959) = 27.080383176 Calculate the square root of the right side: 5.203881549 Break this problem into two subproblems by setting ((x) + 2.244897959) equal to 5.203881549 and -5.203881549.Subproblem 1
(x) + 2.244897959 = 5.203881549 Simplifying (x) + 2.244897959 = 5.203881549 x + 2.244897959 = 5.203881549 Reorder the terms: 2.244897959 + x = 5.203881549 Solving 2.244897959 + x = 5.203881549 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.244897959' to each side of the equation. 2.244897959 + -2.244897959 + x = 5.203881549 + -2.244897959 Combine like terms: 2.244897959 + -2.244897959 = 0.000000000 0.000000000 + x = 5.203881549 + -2.244897959 x = 5.203881549 + -2.244897959 Combine like terms: 5.203881549 + -2.244897959 = 2.95898359 x = 2.95898359 Simplifying x = 2.95898359Subproblem 2
(x) + 2.244897959 = -5.203881549 Simplifying (x) + 2.244897959 = -5.203881549 x + 2.244897959 = -5.203881549 Reorder the terms: 2.244897959 + x = -5.203881549 Solving 2.244897959 + x = -5.203881549 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.244897959' to each side of the equation. 2.244897959 + -2.244897959 + x = -5.203881549 + -2.244897959 Combine like terms: 2.244897959 + -2.244897959 = 0.000000000 0.000000000 + x = -5.203881549 + -2.244897959 x = -5.203881549 + -2.244897959 Combine like terms: -5.203881549 + -2.244897959 = -7.448779508 x = -7.448779508 Simplifying x = -7.448779508Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.95898359, -7.448779508}
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