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Simplifying 4x2 + -46x + 16 = 0 Reorder the terms: 16 + -46x + 4x2 = 0 Solving 16 + -46x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(8 + -23x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(8 + -23x + 2x2)' equal to zero and attempt to solve: Simplifying 8 + -23x + 2x2 = 0 Solving 8 + -23x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 4 + -11.5x + x2 = 0 Move the constant term to the right: Add '-4' to each side of the equation. 4 + -11.5x + -4 + x2 = 0 + -4 Reorder the terms: 4 + -4 + -11.5x + x2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -11.5x + x2 = 0 + -4 -11.5x + x2 = 0 + -4 Combine like terms: 0 + -4 = -4 -11.5x + x2 = -4 The x term is -11.5x. Take half its coefficient (-5.75). Square it (33.0625) and add it to both sides. Add '33.0625' to each side of the equation. -11.5x + 33.0625 + x2 = -4 + 33.0625 Reorder the terms: 33.0625 + -11.5x + x2 = -4 + 33.0625 Combine like terms: -4 + 33.0625 = 29.0625 33.0625 + -11.5x + x2 = 29.0625 Factor a perfect square on the left side: (x + -5.75)(x + -5.75) = 29.0625 Calculate the square root of the right side: 5.390964663 Break this problem into two subproblems by setting (x + -5.75) equal to 5.390964663 and -5.390964663.Subproblem 1
x + -5.75 = 5.390964663 Simplifying x + -5.75 = 5.390964663 Reorder the terms: -5.75 + x = 5.390964663 Solving -5.75 + x = 5.390964663 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.75' to each side of the equation. -5.75 + 5.75 + x = 5.390964663 + 5.75 Combine like terms: -5.75 + 5.75 = 0.00 0.00 + x = 5.390964663 + 5.75 x = 5.390964663 + 5.75 Combine like terms: 5.390964663 + 5.75 = 11.140964663 x = 11.140964663 Simplifying x = 11.140964663Subproblem 2
x + -5.75 = -5.390964663 Simplifying x + -5.75 = -5.390964663 Reorder the terms: -5.75 + x = -5.390964663 Solving -5.75 + x = -5.390964663 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.75' to each side of the equation. -5.75 + 5.75 + x = -5.390964663 + 5.75 Combine like terms: -5.75 + 5.75 = 0.00 0.00 + x = -5.390964663 + 5.75 x = -5.390964663 + 5.75 Combine like terms: -5.390964663 + 5.75 = 0.359035337 x = 0.359035337 Simplifying x = 0.359035337Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.140964663, 0.359035337}Solution
x = {11.140964663, 0.359035337}
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