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Simplifying 16x2 + -34x + 18 = 2 Reorder the terms: 18 + -34x + 16x2 = 2 Solving 18 + -34x + 16x2 = 2 Solving for variable 'x'. Reorder the terms: 18 + -2 + -34x + 16x2 = 2 + -2 Combine like terms: 18 + -2 = 16 16 + -34x + 16x2 = 2 + -2 Combine like terms: 2 + -2 = 0 16 + -34x + 16x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(8 + -17x + 8x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(8 + -17x + 8x2)' equal to zero and attempt to solve: Simplifying 8 + -17x + 8x2 = 0 Solving 8 + -17x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 1 + -2.125x + x2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + -2.125x + -1 + x2 = 0 + -1 Reorder the terms: 1 + -1 + -2.125x + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2.125x + x2 = 0 + -1 -2.125x + x2 = 0 + -1 Combine like terms: 0 + -1 = -1 -2.125x + x2 = -1 The x term is -2.125x. Take half its coefficient (-1.0625). Square it (1.12890625) and add it to both sides. Add '1.12890625' to each side of the equation. -2.125x + 1.12890625 + x2 = -1 + 1.12890625 Reorder the terms: 1.12890625 + -2.125x + x2 = -1 + 1.12890625 Combine like terms: -1 + 1.12890625 = 0.12890625 1.12890625 + -2.125x + x2 = 0.12890625 Factor a perfect square on the left side: (x + -1.0625)(x + -1.0625) = 0.12890625 Calculate the square root of the right side: 0.359035165 Break this problem into two subproblems by setting (x + -1.0625) equal to 0.359035165 and -0.359035165.Subproblem 1
x + -1.0625 = 0.359035165 Simplifying x + -1.0625 = 0.359035165 Reorder the terms: -1.0625 + x = 0.359035165 Solving -1.0625 + x = 0.359035165 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.0625' to each side of the equation. -1.0625 + 1.0625 + x = 0.359035165 + 1.0625 Combine like terms: -1.0625 + 1.0625 = 0.0000 0.0000 + x = 0.359035165 + 1.0625 x = 0.359035165 + 1.0625 Combine like terms: 0.359035165 + 1.0625 = 1.421535165 x = 1.421535165 Simplifying x = 1.421535165Subproblem 2
x + -1.0625 = -0.359035165 Simplifying x + -1.0625 = -0.359035165 Reorder the terms: -1.0625 + x = -0.359035165 Solving -1.0625 + x = -0.359035165 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.0625' to each side of the equation. -1.0625 + 1.0625 + x = -0.359035165 + 1.0625 Combine like terms: -1.0625 + 1.0625 = 0.0000 0.0000 + x = -0.359035165 + 1.0625 x = -0.359035165 + 1.0625 Combine like terms: -0.359035165 + 1.0625 = 0.703464835 x = 0.703464835 Simplifying x = 0.703464835Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.421535165, 0.703464835}Solution
x = {1.421535165, 0.703464835}
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