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Simplifying 0 = -16x2 + 155x + -9 Reorder the terms: 0 = -9 + 155x + -16x2 Solving 0 = -9 + 155x + -16x2 Solving for variable 'x'. Combine like terms: 0 + 9 = 9 9 + -155x + 16x2 = -9 + 155x + -16x2 + 9 + -155x + 16x2 Reorder the terms: 9 + -155x + 16x2 = -9 + 9 + 155x + -155x + -16x2 + 16x2 Combine like terms: -9 + 9 = 0 9 + -155x + 16x2 = 0 + 155x + -155x + -16x2 + 16x2 9 + -155x + 16x2 = 155x + -155x + -16x2 + 16x2 Combine like terms: 155x + -155x = 0 9 + -155x + 16x2 = 0 + -16x2 + 16x2 9 + -155x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 9 + -155x + 16x2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 0.5625 + -9.6875x + x2 = 0 Move the constant term to the right: Add '-0.5625' to each side of the equation. 0.5625 + -9.6875x + -0.5625 + x2 = 0 + -0.5625 Reorder the terms: 0.5625 + -0.5625 + -9.6875x + x2 = 0 + -0.5625 Combine like terms: 0.5625 + -0.5625 = 0.0000 0.0000 + -9.6875x + x2 = 0 + -0.5625 -9.6875x + x2 = 0 + -0.5625 Combine like terms: 0 + -0.5625 = -0.5625 -9.6875x + x2 = -0.5625 The x term is -9.6875x. Take half its coefficient (-4.84375). Square it (23.46191406) and add it to both sides. Add '23.46191406' to each side of the equation. -9.6875x + 23.46191406 + x2 = -0.5625 + 23.46191406 Reorder the terms: 23.46191406 + -9.6875x + x2 = -0.5625 + 23.46191406 Combine like terms: -0.5625 + 23.46191406 = 22.89941406 23.46191406 + -9.6875x + x2 = 22.89941406 Factor a perfect square on the left side: (x + -4.84375)(x + -4.84375) = 22.89941406 Calculate the square root of the right side: 4.785333224 Break this problem into two subproblems by setting (x + -4.84375) equal to 4.785333224 and -4.785333224.Subproblem 1
x + -4.84375 = 4.785333224 Simplifying x + -4.84375 = 4.785333224 Reorder the terms: -4.84375 + x = 4.785333224 Solving -4.84375 + x = 4.785333224 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.84375' to each side of the equation. -4.84375 + 4.84375 + x = 4.785333224 + 4.84375 Combine like terms: -4.84375 + 4.84375 = 0.00000 0.00000 + x = 4.785333224 + 4.84375 x = 4.785333224 + 4.84375 Combine like terms: 4.785333224 + 4.84375 = 9.629083224 x = 9.629083224 Simplifying x = 9.629083224Subproblem 2
x + -4.84375 = -4.785333224 Simplifying x + -4.84375 = -4.785333224 Reorder the terms: -4.84375 + x = -4.785333224 Solving -4.84375 + x = -4.785333224 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.84375' to each side of the equation. -4.84375 + 4.84375 + x = -4.785333224 + 4.84375 Combine like terms: -4.84375 + 4.84375 = 0.00000 0.00000 + x = -4.785333224 + 4.84375 x = -4.785333224 + 4.84375 Combine like terms: -4.785333224 + 4.84375 = 0.058416776 x = 0.058416776 Simplifying x = 0.058416776Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.629083224, 0.058416776}
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