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Simplifying 6x2 + -5x + -46 = 5x + -10 Reorder the terms: -46 + -5x + 6x2 = 5x + -10 Reorder the terms: -46 + -5x + 6x2 = -10 + 5x Solving -46 + -5x + 6x2 = -10 + 5x Solving for variable 'x'. Reorder the terms: -46 + 10 + -5x + -5x + 6x2 = -10 + 5x + 10 + -5x Combine like terms: -46 + 10 = -36 -36 + -5x + -5x + 6x2 = -10 + 5x + 10 + -5x Combine like terms: -5x + -5x = -10x -36 + -10x + 6x2 = -10 + 5x + 10 + -5x Reorder the terms: -36 + -10x + 6x2 = -10 + 10 + 5x + -5x Combine like terms: -10 + 10 = 0 -36 + -10x + 6x2 = 0 + 5x + -5x -36 + -10x + 6x2 = 5x + -5x Combine like terms: 5x + -5x = 0 -36 + -10x + 6x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-18 + -5x + 3x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-18 + -5x + 3x2)' equal to zero and attempt to solve: Simplifying -18 + -5x + 3x2 = 0 Solving -18 + -5x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -6 + -1.666666667x + x2 = 0 Move the constant term to the right: Add '6' to each side of the equation. -6 + -1.666666667x + 6 + x2 = 0 + 6 Reorder the terms: -6 + 6 + -1.666666667x + x2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -1.666666667x + x2 = 0 + 6 -1.666666667x + x2 = 0 + 6 Combine like terms: 0 + 6 = 6 -1.666666667x + x2 = 6 The x term is -1.666666667x. Take half its coefficient (-0.8333333335). Square it (0.6944444447) and add it to both sides. Add '0.6944444447' to each side of the equation. -1.666666667x + 0.6944444447 + x2 = 6 + 0.6944444447 Reorder the terms: 0.6944444447 + -1.666666667x + x2 = 6 + 0.6944444447 Combine like terms: 6 + 0.6944444447 = 6.6944444447 0.6944444447 + -1.666666667x + x2 = 6.6944444447 Factor a perfect square on the left side: (x + -0.8333333335)(x + -0.8333333335) = 6.6944444447 Calculate the square root of the right side: 2.587362449 Break this problem into two subproblems by setting (x + -0.8333333335) equal to 2.587362449 and -2.587362449.Subproblem 1
x + -0.8333333335 = 2.587362449 Simplifying x + -0.8333333335 = 2.587362449 Reorder the terms: -0.8333333335 + x = 2.587362449 Solving -0.8333333335 + x = 2.587362449 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8333333335' to each side of the equation. -0.8333333335 + 0.8333333335 + x = 2.587362449 + 0.8333333335 Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000 0.0000000000 + x = 2.587362449 + 0.8333333335 x = 2.587362449 + 0.8333333335 Combine like terms: 2.587362449 + 0.8333333335 = 3.4206957825 x = 3.4206957825 Simplifying x = 3.4206957825Subproblem 2
x + -0.8333333335 = -2.587362449 Simplifying x + -0.8333333335 = -2.587362449 Reorder the terms: -0.8333333335 + x = -2.587362449 Solving -0.8333333335 + x = -2.587362449 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8333333335' to each side of the equation. -0.8333333335 + 0.8333333335 + x = -2.587362449 + 0.8333333335 Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000 0.0000000000 + x = -2.587362449 + 0.8333333335 x = -2.587362449 + 0.8333333335 Combine like terms: -2.587362449 + 0.8333333335 = -1.7540291155 x = -1.7540291155 Simplifying x = -1.7540291155Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.4206957825, -1.7540291155}Solution
x = {3.4206957825, -1.7540291155}
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