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Simplifying 12x2 + 96x + -18 = 0 Reorder the terms: -18 + 96x + 12x2 = 0 Solving -18 + 96x + 12x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '6'. 6(-3 + 16x + 2x2) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(-3 + 16x + 2x2)' equal to zero and attempt to solve: Simplifying -3 + 16x + 2x2 = 0 Solving -3 + 16x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -1.5 + 8x + x2 = 0 Move the constant term to the right: Add '1.5' to each side of the equation. -1.5 + 8x + 1.5 + x2 = 0 + 1.5 Reorder the terms: -1.5 + 1.5 + 8x + x2 = 0 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + 8x + x2 = 0 + 1.5 8x + x2 = 0 + 1.5 Combine like terms: 0 + 1.5 = 1.5 8x + x2 = 1.5 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 = 1.5 + 16 Reorder the terms: 16 + 8x + x2 = 1.5 + 16 Combine like terms: 1.5 + 16 = 17.5 16 + 8x + x2 = 17.5 Factor a perfect square on the left side: (x + 4)(x + 4) = 17.5 Calculate the square root of the right side: 4.183300133 Break this problem into two subproblems by setting (x + 4) equal to 4.183300133 and -4.183300133.Subproblem 1
x + 4 = 4.183300133 Simplifying x + 4 = 4.183300133 Reorder the terms: 4 + x = 4.183300133 Solving 4 + x = 4.183300133 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 = 4.183300133 + -4 Combine like terms: 4 + -4 = 0 0 + x = 4.183300133 + -4 x = 4.183300133 + -4 Combine like terms: 4.183300133 + -4 = 0.183300133 x = 0.183300133 Simplifying x = 0.183300133Subproblem 2
x + 4 = -4.183300133 Simplifying x + 4 = -4.183300133 Reorder the terms: 4 + x = -4.183300133 Solving 4 + x = -4.183300133 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 = -4.183300133 + -4 Combine like terms: 4 + -4 = 0 0 + x = -4.183300133 + -4 x = -4.183300133 + -4 Combine like terms: -4.183300133 + -4 = -8.183300133 x = -8.183300133 Simplifying x = -8.183300133Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.183300133, -8.183300133}Solution
x = {0.183300133, -8.183300133}
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