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Simplifying 0 = 16x2 + -48x + -8 Reorder the terms: 0 = -8 + -48x + 16x2 Solving 0 = -8 + -48x + 16x2 Solving for variable 'x'. Combine like terms: 0 + 8 = 8 8 + 48x + -16x2 = -8 + -48x + 16x2 + 8 + 48x + -16x2 Reorder the terms: 8 + 48x + -16x2 = -8 + 8 + -48x + 48x + 16x2 + -16x2 Combine like terms: -8 + 8 = 0 8 + 48x + -16x2 = 0 + -48x + 48x + 16x2 + -16x2 8 + 48x + -16x2 = -48x + 48x + 16x2 + -16x2 Combine like terms: -48x + 48x = 0 8 + 48x + -16x2 = 0 + 16x2 + -16x2 8 + 48x + -16x2 = 16x2 + -16x2 Combine like terms: 16x2 + -16x2 = 0 8 + 48x + -16x2 = 0 Factor out the Greatest Common Factor (GCF), '8'. 8(1 + 6x + -2x2) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(1 + 6x + -2x2)' equal to zero and attempt to solve: Simplifying 1 + 6x + -2x2 = 0 Solving 1 + 6x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -0.5 + -3x + x2 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + -3x + 0.5 + x2 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + -3x + x2 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + -3x + x2 = 0 + 0.5 -3x + x2 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 -3x + x2 = 0.5 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 = 0.5 + 2.25 Reorder the terms: 2.25 + -3x + x2 = 0.5 + 2.25 Combine like terms: 0.5 + 2.25 = 2.75 2.25 + -3x + x2 = 2.75 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 2.75 Calculate the square root of the right side: 1.658312395 Break this problem into two subproblems by setting (x + -1.5) equal to 1.658312395 and -1.658312395.Subproblem 1
x + -1.5 = 1.658312395 Simplifying x + -1.5 = 1.658312395 Reorder the terms: -1.5 + x = 1.658312395 Solving -1.5 + x = 1.658312395 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 = 1.658312395 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 1.658312395 + 1.5 x = 1.658312395 + 1.5 Combine like terms: 1.658312395 + 1.5 = 3.158312395 x = 3.158312395 Simplifying x = 3.158312395Subproblem 2
x + -1.5 = -1.658312395 Simplifying x + -1.5 = -1.658312395 Reorder the terms: -1.5 + x = -1.658312395 Solving -1.5 + x = -1.658312395 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 = -1.658312395 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -1.658312395 + 1.5 x = -1.658312395 + 1.5 Combine like terms: -1.658312395 + 1.5 = -0.158312395 x = -0.158312395 Simplifying x = -0.158312395Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.158312395, -0.158312395}Solution
x = {3.158312395, -0.158312395}
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