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Simplifying -4.9x2 = -3.6x + -27 Reorder the terms: -4.9x2 = -27 + -3.6x Solving -4.9x2 = -27 + -3.6x Solving for variable 'x'. Reorder the terms: 27 + 3.6x + -4.9x2 = -27 + -3.6x + 27 + 3.6x Reorder the terms: 27 + 3.6x + -4.9x2 = -27 + 27 + -3.6x + 3.6x Combine like terms: -27 + 27 = 0 27 + 3.6x + -4.9x2 = 0 + -3.6x + 3.6x 27 + 3.6x + -4.9x2 = -3.6x + 3.6x Combine like terms: -3.6x + 3.6x = 0.0 27 + 3.6x + -4.9x2 = 0.0 Begin completing the square. Divide all terms by -4.9 the coefficient of the squared term: Divide each side by '-4.9'. -5.510204082 + -0.7346938776x + x2 = 0 Move the constant term to the right: Add '5.510204082' to each side of the equation. -5.510204082 + -0.7346938776x + 5.510204082 + x2 = 0 + 5.510204082 Reorder the terms: -5.510204082 + 5.510204082 + -0.7346938776x + x2 = 0 + 5.510204082 Combine like terms: -5.510204082 + 5.510204082 = 0.000000000 0.000000000 + -0.7346938776x + x2 = 0 + 5.510204082 -0.7346938776x + x2 = 0 + 5.510204082 Combine like terms: 0 + 5.510204082 = 5.510204082 -0.7346938776x + x2 = 5.510204082 The x term is -0.7346938776x. Take half its coefficient (-0.3673469388). Square it (0.1349437734) and add it to both sides. Add '0.1349437734' to each side of the equation. -0.7346938776x + 0.1349437734 + x2 = 5.510204082 + 0.1349437734 Reorder the terms: 0.1349437734 + -0.7346938776x + x2 = 5.510204082 + 0.1349437734 Combine like terms: 5.510204082 + 0.1349437734 = 5.6451478554 0.1349437734 + -0.7346938776x + x2 = 5.6451478554 Factor a perfect square on the left side: (x + -0.3673469388)(x + -0.3673469388) = 5.6451478554 Calculate the square root of the right side: 2.375951989 Break this problem into two subproblems by setting (x + -0.3673469388) equal to 2.375951989 and -2.375951989.Subproblem 1
x + -0.3673469388 = 2.375951989 Simplifying x + -0.3673469388 = 2.375951989 Reorder the terms: -0.3673469388 + x = 2.375951989 Solving -0.3673469388 + x = 2.375951989 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3673469388' to each side of the equation. -0.3673469388 + 0.3673469388 + x = 2.375951989 + 0.3673469388 Combine like terms: -0.3673469388 + 0.3673469388 = 0.0000000000 0.0000000000 + x = 2.375951989 + 0.3673469388 x = 2.375951989 + 0.3673469388 Combine like terms: 2.375951989 + 0.3673469388 = 2.7432989278 x = 2.7432989278 Simplifying x = 2.7432989278Subproblem 2
x + -0.3673469388 = -2.375951989 Simplifying x + -0.3673469388 = -2.375951989 Reorder the terms: -0.3673469388 + x = -2.375951989 Solving -0.3673469388 + x = -2.375951989 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3673469388' to each side of the equation. -0.3673469388 + 0.3673469388 + x = -2.375951989 + 0.3673469388 Combine like terms: -0.3673469388 + 0.3673469388 = 0.0000000000 0.0000000000 + x = -2.375951989 + 0.3673469388 x = -2.375951989 + 0.3673469388 Combine like terms: -2.375951989 + 0.3673469388 = -2.0086050502 x = -2.0086050502 Simplifying x = -2.0086050502Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.7432989278, -2.0086050502}
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