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Simplifying -16x2 + 242x + 149 = 0 Reorder the terms: 149 + 242x + -16x2 = 0 Solving 149 + 242x + -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'. -9.3125 + -15.125x + x2 = 0 Move the constant term to the right: Add '9.3125' to each side of the equation. -9.3125 + -15.125x + 9.3125 + x2 = 0 + 9.3125 Reorder the terms: -9.3125 + 9.3125 + -15.125x + x2 = 0 + 9.3125 Combine like terms: -9.3125 + 9.3125 = 0.0000 0.0000 + -15.125x + x2 = 0 + 9.3125 -15.125x + x2 = 0 + 9.3125 Combine like terms: 0 + 9.3125 = 9.3125 -15.125x + x2 = 9.3125 The x term is -15.125x. Take half its coefficient (-7.5625). Square it (57.19140625) and add it to both sides. Add '57.19140625' to each side of the equation. -15.125x + 57.19140625 + x2 = 9.3125 + 57.19140625 Reorder the terms: 57.19140625 + -15.125x + x2 = 9.3125 + 57.19140625 Combine like terms: 9.3125 + 57.19140625 = 66.50390625 57.19140625 + -15.125x + x2 = 66.50390625 Factor a perfect square on the left side: (x + -7.5625)(x + -7.5625) = 66.50390625 Calculate the square root of the right side: 8.154992719 Break this problem into two subproblems by setting (x + -7.5625) equal to 8.154992719 and -8.154992719.Subproblem 1
x + -7.5625 = 8.154992719 Simplifying x + -7.5625 = 8.154992719 Reorder the terms: -7.5625 + x = 8.154992719 Solving -7.5625 + x = 8.154992719 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.5625' to each side of the equation. -7.5625 + 7.5625 + x = 8.154992719 + 7.5625 Combine like terms: -7.5625 + 7.5625 = 0.0000 0.0000 + x = 8.154992719 + 7.5625 x = 8.154992719 + 7.5625 Combine like terms: 8.154992719 + 7.5625 = 15.717492719 x = 15.717492719 Simplifying x = 15.717492719Subproblem 2
x + -7.5625 = -8.154992719 Simplifying x + -7.5625 = -8.154992719 Reorder the terms: -7.5625 + x = -8.154992719 Solving -7.5625 + x = -8.154992719 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.5625' to each side of the equation. -7.5625 + 7.5625 + x = -8.154992719 + 7.5625 Combine like terms: -7.5625 + 7.5625 = 0.0000 0.0000 + x = -8.154992719 + 7.5625 x = -8.154992719 + 7.5625 Combine like terms: -8.154992719 + 7.5625 = -0.592492719 x = -0.592492719 Simplifying x = -0.592492719Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.717492719, -0.592492719}
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