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Simplifying 16x2 + -96x + 136 = 0 Reorder the terms: 136 + -96x + 16x2 = 0 Solving 136 + -96x + 16x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '8'. 8(17 + -12x + 2x2) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(17 + -12x + 2x2)' equal to zero and attempt to solve: Simplifying 17 + -12x + 2x2 = 0 Solving 17 + -12x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 8.5 + -6x + x2 = 0 Move the constant term to the right: Add '-8.5' to each side of the equation. 8.5 + -6x + -8.5 + x2 = 0 + -8.5 Reorder the terms: 8.5 + -8.5 + -6x + x2 = 0 + -8.5 Combine like terms: 8.5 + -8.5 = 0.0 0.0 + -6x + x2 = 0 + -8.5 -6x + x2 = 0 + -8.5 Combine like terms: 0 + -8.5 = -8.5 -6x + x2 = -8.5 The x term is -6x. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6x + 9 + x2 = -8.5 + 9 Reorder the terms: 9 + -6x + x2 = -8.5 + 9 Combine like terms: -8.5 + 9 = 0.5 9 + -6x + x2 = 0.5 Factor a perfect square on the left side: (x + -3)(x + -3) = 0.5 Calculate the square root of the right side: 0.707106781 Break this problem into two subproblems by setting (x + -3) equal to 0.707106781 and -0.707106781.Subproblem 1
x + -3 = 0.707106781 Simplifying x + -3 = 0.707106781 Reorder the terms: -3 + x = 0.707106781 Solving -3 + x = 0.707106781 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 0.707106781 + 3 Combine like terms: -3 + 3 = 0 0 + x = 0.707106781 + 3 x = 0.707106781 + 3 Combine like terms: 0.707106781 + 3 = 3.707106781 x = 3.707106781 Simplifying x = 3.707106781Subproblem 2
x + -3 = -0.707106781 Simplifying x + -3 = -0.707106781 Reorder the terms: -3 + x = -0.707106781 Solving -3 + x = -0.707106781 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -0.707106781 + 3 Combine like terms: -3 + 3 = 0 0 + x = -0.707106781 + 3 x = -0.707106781 + 3 Combine like terms: -0.707106781 + 3 = 2.292893219 x = 2.292893219 Simplifying x = 2.292893219Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.707106781, 2.292893219}Solution
x = {3.707106781, 2.292893219}
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