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Simplifying 12x + -16x2 + 480 = 0 Reorder the terms: 480 + 12x + -16x2 = 0 Solving 480 + 12x + -16x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(120 + 3x + -4x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(120 + 3x + -4x2)' equal to zero and attempt to solve: Simplifying 120 + 3x + -4x2 = 0 Solving 120 + 3x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -30 + -0.75x + x2 = 0 Move the constant term to the right: Add '30' to each side of the equation. -30 + -0.75x + 30 + x2 = 0 + 30 Reorder the terms: -30 + 30 + -0.75x + x2 = 0 + 30 Combine like terms: -30 + 30 = 0 0 + -0.75x + x2 = 0 + 30 -0.75x + x2 = 0 + 30 Combine like terms: 0 + 30 = 30 -0.75x + x2 = 30 The x term is -0.75x. Take half its coefficient (-0.375). Square it (0.140625) and add it to both sides. Add '0.140625' to each side of the equation. -0.75x + 0.140625 + x2 = 30 + 0.140625 Reorder the terms: 0.140625 + -0.75x + x2 = 30 + 0.140625 Combine like terms: 30 + 0.140625 = 30.140625 0.140625 + -0.75x + x2 = 30.140625 Factor a perfect square on the left side: (x + -0.375)(x + -0.375) = 30.140625 Calculate the square root of the right side: 5.490047814 Break this problem into two subproblems by setting (x + -0.375) equal to 5.490047814 and -5.490047814.Subproblem 1
x + -0.375 = 5.490047814 Simplifying x + -0.375 = 5.490047814 Reorder the terms: -0.375 + x = 5.490047814 Solving -0.375 + x = 5.490047814 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.375' to each side of the equation. -0.375 + 0.375 + x = 5.490047814 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + x = 5.490047814 + 0.375 x = 5.490047814 + 0.375 Combine like terms: 5.490047814 + 0.375 = 5.865047814 x = 5.865047814 Simplifying x = 5.865047814Subproblem 2
x + -0.375 = -5.490047814 Simplifying x + -0.375 = -5.490047814 Reorder the terms: -0.375 + x = -5.490047814 Solving -0.375 + x = -5.490047814 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.375' to each side of the equation. -0.375 + 0.375 + x = -5.490047814 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + x = -5.490047814 + 0.375 x = -5.490047814 + 0.375 Combine like terms: -5.490047814 + 0.375 = -5.115047814 x = -5.115047814 Simplifying x = -5.115047814Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.865047814, -5.115047814}Solution
x = {5.865047814, -5.115047814}
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