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Simplifying 4x2 + -72x + 322 = 0 Reorder the terms: 322 + -72x + 4x2 = 0 Solving 322 + -72x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(161 + -36x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(161 + -36x + 2x2)' equal to zero and attempt to solve: Simplifying 161 + -36x + 2x2 = 0 Solving 161 + -36x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 80.5 + -18x + x2 = 0 Move the constant term to the right: Add '-80.5' to each side of the equation. 80.5 + -18x + -80.5 + x2 = 0 + -80.5 Reorder the terms: 80.5 + -80.5 + -18x + x2 = 0 + -80.5 Combine like terms: 80.5 + -80.5 = 0.0 0.0 + -18x + x2 = 0 + -80.5 -18x + x2 = 0 + -80.5 Combine like terms: 0 + -80.5 = -80.5 -18x + x2 = -80.5 The x term is -18x. Take half its coefficient (-9). Square it (81) and add it to both sides. Add '81' to each side of the equation. -18x + 81 + x2 = -80.5 + 81 Reorder the terms: 81 + -18x + x2 = -80.5 + 81 Combine like terms: -80.5 + 81 = 0.5 81 + -18x + x2 = 0.5 Factor a perfect square on the left side: (x + -9)(x + -9) = 0.5 Calculate the square root of the right side: 0.707106781 Break this problem into two subproblems by setting (x + -9) equal to 0.707106781 and -0.707106781.Subproblem 1
x + -9 = 0.707106781 Simplifying x + -9 = 0.707106781 Reorder the terms: -9 + x = 0.707106781 Solving -9 + x = 0.707106781 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + x = 0.707106781 + 9 Combine like terms: -9 + 9 = 0 0 + x = 0.707106781 + 9 x = 0.707106781 + 9 Combine like terms: 0.707106781 + 9 = 9.707106781 x = 9.707106781 Simplifying x = 9.707106781Subproblem 2
x + -9 = -0.707106781 Simplifying x + -9 = -0.707106781 Reorder the terms: -9 + x = -0.707106781 Solving -9 + x = -0.707106781 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + x = -0.707106781 + 9 Combine like terms: -9 + 9 = 0 0 + x = -0.707106781 + 9 x = -0.707106781 + 9 Combine like terms: -0.707106781 + 9 = 8.292893219 x = 8.292893219 Simplifying x = 8.292893219Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.707106781, 8.292893219}Solution
x = {9.707106781, 8.292893219}
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