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Simplifying 16x2 + -144x + -165 = 0 Reorder the terms: -165 + -144x + 16x2 = 0 Solving -165 + -144x + 16x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -10.3125 + -9x + x2 = 0 Move the constant term to the right: Add '10.3125' to each side of the equation. -10.3125 + -9x + 10.3125 + x2 = 0 + 10.3125 Reorder the terms: -10.3125 + 10.3125 + -9x + x2 = 0 + 10.3125 Combine like terms: -10.3125 + 10.3125 = 0.0000 0.0000 + -9x + x2 = 0 + 10.3125 -9x + x2 = 0 + 10.3125 Combine like terms: 0 + 10.3125 = 10.3125 -9x + x2 = 10.3125 The x term is -9x. Take half its coefficient (-4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. -9x + 20.25 + x2 = 10.3125 + 20.25 Reorder the terms: 20.25 + -9x + x2 = 10.3125 + 20.25 Combine like terms: 10.3125 + 20.25 = 30.5625 20.25 + -9x + x2 = 30.5625 Factor a perfect square on the left side: (x + -4.5)(x + -4.5) = 30.5625 Calculate the square root of the right side: 5.528336097 Break this problem into two subproblems by setting (x + -4.5) equal to 5.528336097 and -5.528336097.Subproblem 1
x + -4.5 = 5.528336097 Simplifying x + -4.5 = 5.528336097 Reorder the terms: -4.5 + x = 5.528336097 Solving -4.5 + x = 5.528336097 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x = 5.528336097 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = 5.528336097 + 4.5 x = 5.528336097 + 4.5 Combine like terms: 5.528336097 + 4.5 = 10.028336097 x = 10.028336097 Simplifying x = 10.028336097Subproblem 2
x + -4.5 = -5.528336097 Simplifying x + -4.5 = -5.528336097 Reorder the terms: -4.5 + x = -5.528336097 Solving -4.5 + x = -5.528336097 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x = -5.528336097 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = -5.528336097 + 4.5 x = -5.528336097 + 4.5 Combine like terms: -5.528336097 + 4.5 = -1.028336097 x = -1.028336097 Simplifying x = -1.028336097Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.028336097, -1.028336097}
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