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Simplifying x = -4.9x2 + 33.6x + 4.9 Reorder the terms: x = 4.9 + 33.6x + -4.9x2 Solving x = 4.9 + 33.6x + -4.9x2 Solving for variable 'x'. Reorder the terms: -4.9 + x + -33.6x + 4.9x2 = 4.9 + 33.6x + -4.9x2 + -4.9 + -33.6x + 4.9x2 Combine like terms: x + -33.6x = -32.6x -4.9 + -32.6x + 4.9x2 = 4.9 + 33.6x + -4.9x2 + -4.9 + -33.6x + 4.9x2 Reorder the terms: -4.9 + -32.6x + 4.9x2 = 4.9 + -4.9 + 33.6x + -33.6x + -4.9x2 + 4.9x2 Combine like terms: 4.9 + -4.9 = 0.0 -4.9 + -32.6x + 4.9x2 = 0.0 + 33.6x + -33.6x + -4.9x2 + 4.9x2 -4.9 + -32.6x + 4.9x2 = 33.6x + -33.6x + -4.9x2 + 4.9x2 Combine like terms: 33.6x + -33.6x = 0.0 -4.9 + -32.6x + 4.9x2 = 0.0 + -4.9x2 + 4.9x2 -4.9 + -32.6x + 4.9x2 = -4.9x2 + 4.9x2 Combine like terms: -4.9x2 + 4.9x2 = 0.0 -4.9 + -32.6x + 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'. -1 + -6.653061224x + x2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + -6.653061224x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + -6.653061224x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -6.653061224x + x2 = 0 + 1 -6.653061224x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 -6.653061224x + x2 = 1 The x term is -6.653061224x. Take half its coefficient (-3.326530612). Square it (11.06580591) and add it to both sides. Add '11.06580591' to each side of the equation. -6.653061224x + 11.06580591 + x2 = 1 + 11.06580591 Reorder the terms: 11.06580591 + -6.653061224x + x2 = 1 + 11.06580591 Combine like terms: 1 + 11.06580591 = 12.06580591 11.06580591 + -6.653061224x + x2 = 12.06580591 Factor a perfect square on the left side: (x + -3.326530612)(x + -3.326530612) = 12.06580591 Calculate the square root of the right side: 3.473586894 Break this problem into two subproblems by setting (x + -3.326530612) equal to 3.473586894 and -3.473586894.Subproblem 1
x + -3.326530612 = 3.473586894 Simplifying x + -3.326530612 = 3.473586894 Reorder the terms: -3.326530612 + x = 3.473586894 Solving -3.326530612 + x = 3.473586894 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.326530612' to each side of the equation. -3.326530612 + 3.326530612 + x = 3.473586894 + 3.326530612 Combine like terms: -3.326530612 + 3.326530612 = 0.000000000 0.000000000 + x = 3.473586894 + 3.326530612 x = 3.473586894 + 3.326530612 Combine like terms: 3.473586894 + 3.326530612 = 6.800117506 x = 6.800117506 Simplifying x = 6.800117506Subproblem 2
x + -3.326530612 = -3.473586894 Simplifying x + -3.326530612 = -3.473586894 Reorder the terms: -3.326530612 + x = -3.473586894 Solving -3.326530612 + x = -3.473586894 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.326530612' to each side of the equation. -3.326530612 + 3.326530612 + x = -3.473586894 + 3.326530612 Combine like terms: -3.326530612 + 3.326530612 = 0.000000000 0.000000000 + x = -3.473586894 + 3.326530612 x = -3.473586894 + 3.326530612 Combine like terms: -3.473586894 + 3.326530612 = -0.147056282 x = -0.147056282 Simplifying x = -0.147056282Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.800117506, -0.147056282}
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