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Simplifying 16x(22x + -1) = 231 Reorder the terms: 16x(-1 + 22x) = 231 (-1 * 16x + 22x * 16x) = 231 (-16x + 352x2) = 231 Solving -16x + 352x2 = 231 Solving for variable 'x'. Reorder the terms: -231 + -16x + 352x2 = 231 + -231 Combine like terms: 231 + -231 = 0 -231 + -16x + 352x2 = 0 Begin completing the square. Divide all terms by 352 the coefficient of the squared term: Divide each side by '352'. -0.65625 + -0.04545454545x + x2 = 0 Move the constant term to the right: Add '0.65625' to each side of the equation. -0.65625 + -0.04545454545x + 0.65625 + x2 = 0 + 0.65625 Reorder the terms: -0.65625 + 0.65625 + -0.04545454545x + x2 = 0 + 0.65625 Combine like terms: -0.65625 + 0.65625 = 0.00000 0.00000 + -0.04545454545x + x2 = 0 + 0.65625 -0.04545454545x + x2 = 0 + 0.65625 Combine like terms: 0 + 0.65625 = 0.65625 -0.04545454545x + x2 = 0.65625 The x term is -0.04545454545x. Take half its coefficient (-0.02272727273). Square it (0.0005165289257) and add it to both sides. Add '0.0005165289257' to each side of the equation. -0.04545454545x + 0.0005165289257 + x2 = 0.65625 + 0.0005165289257 Reorder the terms: 0.0005165289257 + -0.04545454545x + x2 = 0.65625 + 0.0005165289257 Combine like terms: 0.65625 + 0.0005165289257 = 0.6567665289257 0.0005165289257 + -0.04545454545x + x2 = 0.6567665289257 Factor a perfect square on the left side: (x + -0.02272727273)(x + -0.02272727273) = 0.6567665289257 Calculate the square root of the right side: 0.810411333 Break this problem into two subproblems by setting (x + -0.02272727273) equal to 0.810411333 and -0.810411333.Subproblem 1
x + -0.02272727273 = 0.810411333 Simplifying x + -0.02272727273 = 0.810411333 Reorder the terms: -0.02272727273 + x = 0.810411333 Solving -0.02272727273 + x = 0.810411333 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.02272727273' to each side of the equation. -0.02272727273 + 0.02272727273 + x = 0.810411333 + 0.02272727273 Combine like terms: -0.02272727273 + 0.02272727273 = 0.00000000000 0.00000000000 + x = 0.810411333 + 0.02272727273 x = 0.810411333 + 0.02272727273 Combine like terms: 0.810411333 + 0.02272727273 = 0.83313860573 x = 0.83313860573 Simplifying x = 0.83313860573Subproblem 2
x + -0.02272727273 = -0.810411333 Simplifying x + -0.02272727273 = -0.810411333 Reorder the terms: -0.02272727273 + x = -0.810411333 Solving -0.02272727273 + x = -0.810411333 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.02272727273' to each side of the equation. -0.02272727273 + 0.02272727273 + x = -0.810411333 + 0.02272727273 Combine like terms: -0.02272727273 + 0.02272727273 = 0.00000000000 0.00000000000 + x = -0.810411333 + 0.02272727273 x = -0.810411333 + 0.02272727273 Combine like terms: -0.810411333 + 0.02272727273 = -0.78768406027 x = -0.78768406027 Simplifying x = -0.78768406027Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.83313860573, -0.78768406027}
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