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Simplifying 3x2 + -48x + -18 = 0 Reorder the terms: -18 + -48x + 3x2 = 0 Solving -18 + -48x + 3x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(-6 + -16x + x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-6 + -16x + x2)' equal to zero and attempt to solve: Simplifying -6 + -16x + x2 = 0 Solving -6 + -16x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '6' to each side of the equation. -6 + -16x + 6 + x2 = 0 + 6 Reorder the terms: -6 + 6 + -16x + x2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -16x + x2 = 0 + 6 -16x + x2 = 0 + 6 Combine like terms: 0 + 6 = 6 -16x + x2 = 6 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 = 6 + 64 Reorder the terms: 64 + -16x + x2 = 6 + 64 Combine like terms: 6 + 64 = 70 64 + -16x + x2 = 70 Factor a perfect square on the left side: (x + -8)(x + -8) = 70 Calculate the square root of the right side: 8.366600265 Break this problem into two subproblems by setting (x + -8) equal to 8.366600265 and -8.366600265.Subproblem 1
x + -8 = 8.366600265 Simplifying x + -8 = 8.366600265 Reorder the terms: -8 + x = 8.366600265 Solving -8 + x = 8.366600265 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 = 8.366600265 + 8 Combine like terms: -8 + 8 = 0 0 + x = 8.366600265 + 8 x = 8.366600265 + 8 Combine like terms: 8.366600265 + 8 = 16.366600265 x = 16.366600265 Simplifying x = 16.366600265Subproblem 2
x + -8 = -8.366600265 Simplifying x + -8 = -8.366600265 Reorder the terms: -8 + x = -8.366600265 Solving -8 + x = -8.366600265 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 = -8.366600265 + 8 Combine like terms: -8 + 8 = 0 0 + x = -8.366600265 + 8 x = -8.366600265 + 8 Combine like terms: -8.366600265 + 8 = -0.366600265 x = -0.366600265 Simplifying x = -0.366600265Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.366600265, -0.366600265}Solution
x = {16.366600265, -0.366600265}
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