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Simplifying 20 = 6x2 + 10x + -16 Reorder the terms: 20 = -16 + 10x + 6x2 Solving 20 = -16 + 10x + 6x2 Solving for variable 'x'. Combine like terms: 20 + 16 = 36 36 + -10x + -6x2 = -16 + 10x + 6x2 + 16 + -10x + -6x2 Reorder the terms: 36 + -10x + -6x2 = -16 + 16 + 10x + -10x + 6x2 + -6x2 Combine like terms: -16 + 16 = 0 36 + -10x + -6x2 = 0 + 10x + -10x + 6x2 + -6x2 36 + -10x + -6x2 = 10x + -10x + 6x2 + -6x2 Combine like terms: 10x + -10x = 0 36 + -10x + -6x2 = 0 + 6x2 + -6x2 36 + -10x + -6x2 = 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 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 = 1.7540291155 x = 1.7540291155 Simplifying x = 1.7540291155Subproblem 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 = -3.4206957825 x = -3.4206957825 Simplifying x = -3.4206957825Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.7540291155, -3.4206957825}Solution
x = {1.7540291155, -3.4206957825}
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