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Simplifying 64x2 + -116x + 22 = 0 Reorder the terms: 22 + -116x + 64x2 = 0 Solving 22 + -116x + 64x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(11 + -58x + 32x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(11 + -58x + 32x2)' equal to zero and attempt to solve: Simplifying 11 + -58x + 32x2 = 0 Solving 11 + -58x + 32x2 = 0 Begin completing the square. Divide all terms by 32 the coefficient of the squared term: Divide each side by '32'. 0.34375 + -1.8125x + x2 = 0 Move the constant term to the right: Add '-0.34375' to each side of the equation. 0.34375 + -1.8125x + -0.34375 + x2 = 0 + -0.34375 Reorder the terms: 0.34375 + -0.34375 + -1.8125x + x2 = 0 + -0.34375 Combine like terms: 0.34375 + -0.34375 = 0.00000 0.00000 + -1.8125x + x2 = 0 + -0.34375 -1.8125x + x2 = 0 + -0.34375 Combine like terms: 0 + -0.34375 = -0.34375 -1.8125x + x2 = -0.34375 The x term is -1.8125x. Take half its coefficient (-0.90625). Square it (0.8212890625) and add it to both sides. Add '0.8212890625' to each side of the equation. -1.8125x + 0.8212890625 + x2 = -0.34375 + 0.8212890625 Reorder the terms: 0.8212890625 + -1.8125x + x2 = -0.34375 + 0.8212890625 Combine like terms: -0.34375 + 0.8212890625 = 0.4775390625 0.8212890625 + -1.8125x + x2 = 0.4775390625 Factor a perfect square on the left side: (x + -0.90625)(x + -0.90625) = 0.4775390625 Calculate the square root of the right side: 0.691042012 Break this problem into two subproblems by setting (x + -0.90625) equal to 0.691042012 and -0.691042012.Subproblem 1
x + -0.90625 = 0.691042012 Simplifying x + -0.90625 = 0.691042012 Reorder the terms: -0.90625 + x = 0.691042012 Solving -0.90625 + x = 0.691042012 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.90625' to each side of the equation. -0.90625 + 0.90625 + x = 0.691042012 + 0.90625 Combine like terms: -0.90625 + 0.90625 = 0.00000 0.00000 + x = 0.691042012 + 0.90625 x = 0.691042012 + 0.90625 Combine like terms: 0.691042012 + 0.90625 = 1.597292012 x = 1.597292012 Simplifying x = 1.597292012Subproblem 2
x + -0.90625 = -0.691042012 Simplifying x + -0.90625 = -0.691042012 Reorder the terms: -0.90625 + x = -0.691042012 Solving -0.90625 + x = -0.691042012 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.90625' to each side of the equation. -0.90625 + 0.90625 + x = -0.691042012 + 0.90625 Combine like terms: -0.90625 + 0.90625 = 0.00000 0.00000 + x = -0.691042012 + 0.90625 x = -0.691042012 + 0.90625 Combine like terms: -0.691042012 + 0.90625 = 0.215207988 x = 0.215207988 Simplifying x = 0.215207988Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.597292012, 0.215207988}Solution
x = {1.597292012, 0.215207988}
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