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Simplifying 0 = (-16x2) + 48x + 6 Reorder the terms: 0 = 6 + 48x + (-16x2) Solving 0 = 6 + 48x + (-16x2) Solving for variable 'x'. Combine like terms: 0 + -6 = -6 -6 + -48x + (16x2) = 6 + 48x + (-16x2) + -6 + -48x + (16x2) Reorder the terms: -6 + -48x + (16x2) = 6 + -6 + 48x + -48x + (-16x2) + (16x2) Combine like terms: 6 + -6 = 0 -6 + -48x + (16x2) = 0 + 48x + -48x + (-16x2) + (16x2) -6 + -48x + (16x2) = 48x + -48x + (-16x2) + (16x2) Combine like terms: 48x + -48x = 0 -6 + -48x + (16x2) = 0 + (-16x2) + (16x2) -6 + -48x + (16x2) = (-16x2) + (16x2) Combine like terms: (-16x2) + (16x2) = 0 -6 + -48x + (16x2) = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-3 + -24x + (8x2)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-3 + -24x + (8x2))' equal to zero and attempt to solve: Simplifying -3 + -24x + (8x2) = 0 Solving -3 + -24x + (8x2) = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -0.375 + -3x + x2 = 0 Move the constant term to the right: Add '0.375' to each side of the equation. -0.375 + -3x + 0.375 + x2 = 0 + 0.375 Reorder the terms: -0.375 + 0.375 + -3x + x2 = 0 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + -3x + x2 = 0 + 0.375 -3x + x2 = 0 + 0.375 Combine like terms: 0 + 0.375 = 0.375 -3x + x2 = 0.375 The x term is -3x. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3x + 2.25 + x2 = 0.375 + 2.25 Reorder the terms: 2.25 + -3x + x2 = 0.375 + 2.25 Combine like terms: 0.375 + 2.25 = 2.625 2.25 + -3x + x2 = 2.625 Factor a perfect square on the left side: ((x) + -1.5)((x) + -1.5) = 2.625 Calculate the square root of the right side: 1.620185175 Break this problem into two subproblems by setting ((x) + -1.5) equal to 1.620185175 and -1.620185175.Subproblem 1
(x) + -1.5 = 1.620185175 Simplifying (x) + -1.5 = 1.620185175 x + -1.5 = 1.620185175 Reorder the terms: -1.5 + x = 1.620185175 Solving -1.5 + x = 1.620185175 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = 1.620185175 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 1.620185175 + 1.5 x = 1.620185175 + 1.5 Combine like terms: 1.620185175 + 1.5 = 3.120185175 x = 3.120185175 Simplifying x = 3.120185175Subproblem 2
(x) + -1.5 = -1.620185175 Simplifying (x) + -1.5 = -1.620185175 x + -1.5 = -1.620185175 Reorder the terms: -1.5 + x = -1.620185175 Solving -1.5 + x = -1.620185175 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = -1.620185175 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -1.620185175 + 1.5 x = -1.620185175 + 1.5 Combine like terms: -1.620185175 + 1.5 = -0.120185175 x = -0.120185175 Simplifying x = -0.120185175Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.120185175, -0.120185175}Solution
x = {3.120185175, -0.120185175}
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