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Simplifying 0 = 3x2 + 48x + 6 Reorder the terms: 0 = 6 + 48x + 3x2 Solving 0 = 6 + 48x + 3x2 Solving for variable 'x'. Combine like terms: 0 + -6 = -6 -6 + -48x + -3x2 = 6 + 48x + 3x2 + -6 + -48x + -3x2 Reorder the terms: -6 + -48x + -3x2 = 6 + -6 + 48x + -48x + 3x2 + -3x2 Combine like terms: 6 + -6 = 0 -6 + -48x + -3x2 = 0 + 48x + -48x + 3x2 + -3x2 -6 + -48x + -3x2 = 48x + -48x + 3x2 + -3x2 Combine like terms: 48x + -48x = 0 -6 + -48x + -3x2 = 0 + 3x2 + -3x2 -6 + -48x + -3x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 -6 + -48x + -3x2 = 0 Factor out the Greatest Common Factor (GCF), '-3'. -3(2 + 16x + x2) = 0 Ignore the factor -3.Subproblem 1
Set the factor '(2 + 16x + x2)' equal to zero and attempt to solve: Simplifying 2 + 16x + x2 = 0 Solving 2 + 16x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-2' to each side of the equation. 2 + 16x + -2 + x2 = 0 + -2 Reorder the terms: 2 + -2 + 16x + x2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 16x + x2 = 0 + -2 16x + x2 = 0 + -2 Combine like terms: 0 + -2 = -2 16x + x2 = -2 The x term is 16x. Take half its coefficient (8). Square it (64) and add it to both sides. Add '64' to each side of the equation. 16x + 64 + x2 = -2 + 64 Reorder the terms: 64 + 16x + x2 = -2 + 64 Combine like terms: -2 + 64 = 62 64 + 16x + x2 = 62 Factor a perfect square on the left side: (x + 8)(x + 8) = 62 Calculate the square root of the right side: 7.874007874 Break this problem into two subproblems by setting (x + 8) equal to 7.874007874 and -7.874007874.Subproblem 1
x + 8 = 7.874007874 Simplifying x + 8 = 7.874007874 Reorder the terms: 8 + x = 7.874007874 Solving 8 + x = 7.874007874 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + x = 7.874007874 + -8 Combine like terms: 8 + -8 = 0 0 + x = 7.874007874 + -8 x = 7.874007874 + -8 Combine like terms: 7.874007874 + -8 = -0.125992126 x = -0.125992126 Simplifying x = -0.125992126Subproblem 2
x + 8 = -7.874007874 Simplifying x + 8 = -7.874007874 Reorder the terms: 8 + x = -7.874007874 Solving 8 + x = -7.874007874 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + x = -7.874007874 + -8 Combine like terms: 8 + -8 = 0 0 + x = -7.874007874 + -8 x = -7.874007874 + -8 Combine like terms: -7.874007874 + -8 = -15.874007874 x = -15.874007874 Simplifying x = -15.874007874Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.125992126, -15.874007874}Solution
x = {-0.125992126, -15.874007874}
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