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Simplifying 3x + -3(5x2 + -8) + -1(-4x2 + x + -3) = 0 Reorder the terms: 3x + -3(-8 + 5x2) + -1(-4x2 + x + -3) = 0 3x + (-8 * -3 + 5x2 * -3) + -1(-4x2 + x + -3) = 0 3x + (24 + -15x2) + -1(-4x2 + x + -3) = 0 Reorder the terms: 3x + 24 + -15x2 + -1(-3 + x + -4x2) = 0 3x + 24 + -15x2 + (-3 * -1 + x * -1 + -4x2 * -1) = 0 3x + 24 + -15x2 + (3 + -1x + 4x2) = 0 Reorder the terms: 24 + 3 + 3x + -1x + -15x2 + 4x2 = 0 Combine like terms: 24 + 3 = 27 27 + 3x + -1x + -15x2 + 4x2 = 0 Combine like terms: 3x + -1x = 2x 27 + 2x + -15x2 + 4x2 = 0 Combine like terms: -15x2 + 4x2 = -11x2 27 + 2x + -11x2 = 0 Solving 27 + 2x + -11x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -11 the coefficient of the squared term: Divide each side by '-11'. -2.454545455 + -0.1818181818x + x2 = 0 Move the constant term to the right: Add '2.454545455' to each side of the equation. -2.454545455 + -0.1818181818x + 2.454545455 + x2 = 0 + 2.454545455 Reorder the terms: -2.454545455 + 2.454545455 + -0.1818181818x + x2 = 0 + 2.454545455 Combine like terms: -2.454545455 + 2.454545455 = 0.000000000 0.000000000 + -0.1818181818x + x2 = 0 + 2.454545455 -0.1818181818x + x2 = 0 + 2.454545455 Combine like terms: 0 + 2.454545455 = 2.454545455 -0.1818181818x + x2 = 2.454545455 The x term is -0.1818181818x. Take half its coefficient (-0.0909090909). Square it (0.008264462808) and add it to both sides. Add '0.008264462808' to each side of the equation. -0.1818181818x + 0.008264462808 + x2 = 2.454545455 + 0.008264462808 Reorder the terms: 0.008264462808 + -0.1818181818x + x2 = 2.454545455 + 0.008264462808 Combine like terms: 2.454545455 + 0.008264462808 = 2.462809917808 0.008264462808 + -0.1818181818x + x2 = 2.462809917808 Factor a perfect square on the left side: (x + -0.0909090909)(x + -0.0909090909) = 2.462809917808 Calculate the square root of the right side: 1.569334228 Break this problem into two subproblems by setting (x + -0.0909090909) equal to 1.569334228 and -1.569334228.Subproblem 1
x + -0.0909090909 = 1.569334228 Simplifying x + -0.0909090909 = 1.569334228 Reorder the terms: -0.0909090909 + x = 1.569334228 Solving -0.0909090909 + x = 1.569334228 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.0909090909' to each side of the equation. -0.0909090909 + 0.0909090909 + x = 1.569334228 + 0.0909090909 Combine like terms: -0.0909090909 + 0.0909090909 = 0.0000000000 0.0000000000 + x = 1.569334228 + 0.0909090909 x = 1.569334228 + 0.0909090909 Combine like terms: 1.569334228 + 0.0909090909 = 1.6602433189 x = 1.6602433189 Simplifying x = 1.6602433189Subproblem 2
x + -0.0909090909 = -1.569334228 Simplifying x + -0.0909090909 = -1.569334228 Reorder the terms: -0.0909090909 + x = -1.569334228 Solving -0.0909090909 + x = -1.569334228 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.0909090909' to each side of the equation. -0.0909090909 + 0.0909090909 + x = -1.569334228 + 0.0909090909 Combine like terms: -0.0909090909 + 0.0909090909 = 0.0000000000 0.0000000000 + x = -1.569334228 + 0.0909090909 x = -1.569334228 + 0.0909090909 Combine like terms: -1.569334228 + 0.0909090909 = -1.4784251371 x = -1.4784251371 Simplifying x = -1.4784251371Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.6602433189, -1.4784251371}
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