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Simplifying 2x2 = -10.7x + -9.2 Reorder the terms: 2x2 = -9.2 + -10.7x Solving 2x2 = -9.2 + -10.7x Solving for variable 'x'. Reorder the terms: 9.2 + 10.7x + 2x2 = -9.2 + -10.7x + 9.2 + 10.7x Reorder the terms: 9.2 + 10.7x + 2x2 = -9.2 + 9.2 + -10.7x + 10.7x Combine like terms: -9.2 + 9.2 = 0.0 9.2 + 10.7x + 2x2 = 0.0 + -10.7x + 10.7x 9.2 + 10.7x + 2x2 = -10.7x + 10.7x Combine like terms: -10.7x + 10.7x = 0.0 9.2 + 10.7x + 2x2 = 0.0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 4.6 + 5.35x + x2 = 0.0 Move the constant term to the right: Add '-4.6' to each side of the equation. 4.6 + 5.35x + -4.6 + x2 = 0.0 + -4.6 Reorder the terms: 4.6 + -4.6 + 5.35x + x2 = 0.0 + -4.6 Combine like terms: 4.6 + -4.6 = 0.0 0.0 + 5.35x + x2 = 0.0 + -4.6 5.35x + x2 = 0.0 + -4.6 Combine like terms: 0.0 + -4.6 = -4.6 5.35x + x2 = -4.6 The x term is 5.35x. Take half its coefficient (2.675). Square it (7.155625) and add it to both sides. Add '7.155625' to each side of the equation. 5.35x + 7.155625 + x2 = -4.6 + 7.155625 Reorder the terms: 7.155625 + 5.35x + x2 = -4.6 + 7.155625 Combine like terms: -4.6 + 7.155625 = 2.555625 7.155625 + 5.35x + x2 = 2.555625 Factor a perfect square on the left side: (x + 2.675)(x + 2.675) = 2.555625 Calculate the square root of the right side: 1.598632228 Break this problem into two subproblems by setting (x + 2.675) equal to 1.598632228 and -1.598632228.Subproblem 1
x + 2.675 = 1.598632228 Simplifying x + 2.675 = 1.598632228 Reorder the terms: 2.675 + x = 1.598632228 Solving 2.675 + x = 1.598632228 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.675' to each side of the equation. 2.675 + -2.675 + x = 1.598632228 + -2.675 Combine like terms: 2.675 + -2.675 = 0.000 0.000 + x = 1.598632228 + -2.675 x = 1.598632228 + -2.675 Combine like terms: 1.598632228 + -2.675 = -1.076367772 x = -1.076367772 Simplifying x = -1.076367772Subproblem 2
x + 2.675 = -1.598632228 Simplifying x + 2.675 = -1.598632228 Reorder the terms: 2.675 + x = -1.598632228 Solving 2.675 + x = -1.598632228 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.675' to each side of the equation. 2.675 + -2.675 + x = -1.598632228 + -2.675 Combine like terms: 2.675 + -2.675 = 0.000 0.000 + x = -1.598632228 + -2.675 x = -1.598632228 + -2.675 Combine like terms: -1.598632228 + -2.675 = -4.273632228 x = -4.273632228 Simplifying x = -4.273632228Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.076367772, -4.273632228}
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