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Simplifying -16x2 + 12x + 24 = 0 Reorder the terms: 24 + 12x + -16x2 = 0 Solving 24 + 12x + -16x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(6 + 3x + -4x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(6 + 3x + -4x2)' equal to zero and attempt to solve: Simplifying 6 + 3x + -4x2 = 0 Solving 6 + 3x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -1.5 + -0.75x + x2 = 0 Move the constant term to the right: Add '1.5' to each side of the equation. -1.5 + -0.75x + 1.5 + x2 = 0 + 1.5 Reorder the terms: -1.5 + 1.5 + -0.75x + x2 = 0 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + -0.75x + x2 = 0 + 1.5 -0.75x + x2 = 0 + 1.5 Combine like terms: 0 + 1.5 = 1.5 -0.75x + x2 = 1.5 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 = 1.5 + 0.140625 Reorder the terms: 0.140625 + -0.75x + x2 = 1.5 + 0.140625 Combine like terms: 1.5 + 0.140625 = 1.640625 0.140625 + -0.75x + x2 = 1.640625 Factor a perfect square on the left side: (x + -0.375)(x + -0.375) = 1.640625 Calculate the square root of the right side: 1.280868846 Break this problem into two subproblems by setting (x + -0.375) equal to 1.280868846 and -1.280868846.Subproblem 1
x + -0.375 = 1.280868846 Simplifying x + -0.375 = 1.280868846 Reorder the terms: -0.375 + x = 1.280868846 Solving -0.375 + x = 1.280868846 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 = 1.280868846 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + x = 1.280868846 + 0.375 x = 1.280868846 + 0.375 Combine like terms: 1.280868846 + 0.375 = 1.655868846 x = 1.655868846 Simplifying x = 1.655868846Subproblem 2
x + -0.375 = -1.280868846 Simplifying x + -0.375 = -1.280868846 Reorder the terms: -0.375 + x = -1.280868846 Solving -0.375 + x = -1.280868846 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 = -1.280868846 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + x = -1.280868846 + 0.375 x = -1.280868846 + 0.375 Combine like terms: -1.280868846 + 0.375 = -0.905868846 x = -0.905868846 Simplifying x = -0.905868846Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.655868846, -0.905868846}Solution
x = {1.655868846, -0.905868846}
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