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Simplifying 0 = 3x2 + 38x + 8 Reorder the terms: 0 = 8 + 38x + 3x2 Solving 0 = 8 + 38x + 3x2 Solving for variable 'x'. Combine like terms: 0 + -8 = -8 -8 + -38x + -3x2 = 8 + 38x + 3x2 + -8 + -38x + -3x2 Reorder the terms: -8 + -38x + -3x2 = 8 + -8 + 38x + -38x + 3x2 + -3x2 Combine like terms: 8 + -8 = 0 -8 + -38x + -3x2 = 0 + 38x + -38x + 3x2 + -3x2 -8 + -38x + -3x2 = 38x + -38x + 3x2 + -3x2 Combine like terms: 38x + -38x = 0 -8 + -38x + -3x2 = 0 + 3x2 + -3x2 -8 + -38x + -3x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 -8 + -38x + -3x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(8 + 38x + 3x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(8 + 38x + 3x2)' equal to zero and attempt to solve: Simplifying 8 + 38x + 3x2 = 0 Solving 8 + 38x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 2.666666667 + 12.66666667x + x2 = 0 Move the constant term to the right: Add '-2.666666667' to each side of the equation. 2.666666667 + 12.66666667x + -2.666666667 + x2 = 0 + -2.666666667 Reorder the terms: 2.666666667 + -2.666666667 + 12.66666667x + x2 = 0 + -2.666666667 Combine like terms: 2.666666667 + -2.666666667 = 0.000000000 0.000000000 + 12.66666667x + x2 = 0 + -2.666666667 12.66666667x + x2 = 0 + -2.666666667 Combine like terms: 0 + -2.666666667 = -2.666666667 12.66666667x + x2 = -2.666666667 The x term is 12.66666667x. Take half its coefficient (6.333333335). Square it (40.11111113) and add it to both sides. Add '40.11111113' to each side of the equation. 12.66666667x + 40.11111113 + x2 = -2.666666667 + 40.11111113 Reorder the terms: 40.11111113 + 12.66666667x + x2 = -2.666666667 + 40.11111113 Combine like terms: -2.666666667 + 40.11111113 = 37.444444463 40.11111113 + 12.66666667x + x2 = 37.444444463 Factor a perfect square on the left side: (x + 6.333333335)(x + 6.333333335) = 37.444444463 Calculate the square root of the right side: 6.119186585 Break this problem into two subproblems by setting (x + 6.333333335) equal to 6.119186585 and -6.119186585.Subproblem 1
x + 6.333333335 = 6.119186585 Simplifying x + 6.333333335 = 6.119186585 Reorder the terms: 6.333333335 + x = 6.119186585 Solving 6.333333335 + x = 6.119186585 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.333333335' to each side of the equation. 6.333333335 + -6.333333335 + x = 6.119186585 + -6.333333335 Combine like terms: 6.333333335 + -6.333333335 = 0.000000000 0.000000000 + x = 6.119186585 + -6.333333335 x = 6.119186585 + -6.333333335 Combine like terms: 6.119186585 + -6.333333335 = -0.21414675 x = -0.21414675 Simplifying x = -0.21414675Subproblem 2
x + 6.333333335 = -6.119186585 Simplifying x + 6.333333335 = -6.119186585 Reorder the terms: 6.333333335 + x = -6.119186585 Solving 6.333333335 + x = -6.119186585 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.333333335' to each side of the equation. 6.333333335 + -6.333333335 + x = -6.119186585 + -6.333333335 Combine like terms: 6.333333335 + -6.333333335 = 0.000000000 0.000000000 + x = -6.119186585 + -6.333333335 x = -6.119186585 + -6.333333335 Combine like terms: -6.119186585 + -6.333333335 = -12.45251992 x = -12.45251992 Simplifying x = -12.45251992Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.21414675, -12.45251992}Solution
x = {-0.21414675, -12.45251992}
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