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Simplifying -1x + -4(9x2 + 30x + -24) = 0 Reorder the terms: -1x + -4(-24 + 30x + 9x2) = 0 -1x + (-24 * -4 + 30x * -4 + 9x2 * -4) = 0 -1x + (96 + -120x + -36x2) = 0 Reorder the terms: 96 + -1x + -120x + -36x2 = 0 Combine like terms: -1x + -120x = -121x 96 + -121x + -36x2 = 0 Solving 96 + -121x + -36x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -36 the coefficient of the squared term: Divide each side by '-36'. -2.666666667 + 3.361111111x + x2 = 0 Move the constant term to the right: Add '2.666666667' to each side of the equation. -2.666666667 + 3.361111111x + 2.666666667 + x2 = 0 + 2.666666667 Reorder the terms: -2.666666667 + 2.666666667 + 3.361111111x + x2 = 0 + 2.666666667 Combine like terms: -2.666666667 + 2.666666667 = 0.000000000 0.000000000 + 3.361111111x + x2 = 0 + 2.666666667 3.361111111x + x2 = 0 + 2.666666667 Combine like terms: 0 + 2.666666667 = 2.666666667 3.361111111x + x2 = 2.666666667 The x term is 3.361111111x. Take half its coefficient (1.680555556). Square it (2.824266977) and add it to both sides. Add '2.824266977' to each side of the equation. 3.361111111x + 2.824266977 + x2 = 2.666666667 + 2.824266977 Reorder the terms: 2.824266977 + 3.361111111x + x2 = 2.666666667 + 2.824266977 Combine like terms: 2.666666667 + 2.824266977 = 5.490933644 2.824266977 + 3.361111111x + x2 = 5.490933644 Factor a perfect square on the left side: (x + 1.680555556)(x + 1.680555556) = 5.490933644 Calculate the square root of the right side: 2.343274129 Break this problem into two subproblems by setting (x + 1.680555556) equal to 2.343274129 and -2.343274129.Subproblem 1
x + 1.680555556 = 2.343274129 Simplifying x + 1.680555556 = 2.343274129 Reorder the terms: 1.680555556 + x = 2.343274129 Solving 1.680555556 + x = 2.343274129 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.680555556' to each side of the equation. 1.680555556 + -1.680555556 + x = 2.343274129 + -1.680555556 Combine like terms: 1.680555556 + -1.680555556 = 0.000000000 0.000000000 + x = 2.343274129 + -1.680555556 x = 2.343274129 + -1.680555556 Combine like terms: 2.343274129 + -1.680555556 = 0.662718573 x = 0.662718573 Simplifying x = 0.662718573Subproblem 2
x + 1.680555556 = -2.343274129 Simplifying x + 1.680555556 = -2.343274129 Reorder the terms: 1.680555556 + x = -2.343274129 Solving 1.680555556 + x = -2.343274129 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.680555556' to each side of the equation. 1.680555556 + -1.680555556 + x = -2.343274129 + -1.680555556 Combine like terms: 1.680555556 + -1.680555556 = 0.000000000 0.000000000 + x = -2.343274129 + -1.680555556 x = -2.343274129 + -1.680555556 Combine like terms: -2.343274129 + -1.680555556 = -4.023829685 x = -4.023829685 Simplifying x = -4.023829685Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.662718573, -4.023829685}
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