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Simplifying 24x + 12 + -3x2 = 0 Reorder the terms: 12 + 24x + -3x2 = 0 Solving 12 + 24x + -3x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(4 + 8x + -1x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(4 + 8x + -1x2)' equal to zero and attempt to solve: Simplifying 4 + 8x + -1x2 = 0 Solving 4 + 8x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -4 + -8x + x2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + -8x + 4 + x2 = 0 + 4 Reorder the terms: -4 + 4 + -8x + x2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -8x + x2 = 0 + 4 -8x + x2 = 0 + 4 Combine like terms: 0 + 4 = 4 -8x + x2 = 4 The x term is -8x. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8x + 16 + x2 = 4 + 16 Reorder the terms: 16 + -8x + x2 = 4 + 16 Combine like terms: 4 + 16 = 20 16 + -8x + x2 = 20 Factor a perfect square on the left side: (x + -4)(x + -4) = 20 Calculate the square root of the right side: 4.472135955 Break this problem into two subproblems by setting (x + -4) equal to 4.472135955 and -4.472135955.Subproblem 1
x + -4 = 4.472135955 Simplifying x + -4 = 4.472135955 Reorder the terms: -4 + x = 4.472135955 Solving -4 + x = 4.472135955 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 4.472135955 + 4 Combine like terms: -4 + 4 = 0 0 + x = 4.472135955 + 4 x = 4.472135955 + 4 Combine like terms: 4.472135955 + 4 = 8.472135955 x = 8.472135955 Simplifying x = 8.472135955Subproblem 2
x + -4 = -4.472135955 Simplifying x + -4 = -4.472135955 Reorder the terms: -4 + x = -4.472135955 Solving -4 + x = -4.472135955 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = -4.472135955 + 4 Combine like terms: -4 + 4 = 0 0 + x = -4.472135955 + 4 x = -4.472135955 + 4 Combine like terms: -4.472135955 + 4 = -0.472135955 x = -0.472135955 Simplifying x = -0.472135955Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.472135955, -0.472135955}Solution
x = {8.472135955, -0.472135955}
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