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Simplifying -16x2 + -11x + 100 = 0 Reorder the terms: 100 + -11x + -16x2 = 0 Solving 100 + -11x + -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'. -6.25 + 0.6875x + x2 = 0 Move the constant term to the right: Add '6.25' to each side of the equation. -6.25 + 0.6875x + 6.25 + x2 = 0 + 6.25 Reorder the terms: -6.25 + 6.25 + 0.6875x + x2 = 0 + 6.25 Combine like terms: -6.25 + 6.25 = 0.00 0.00 + 0.6875x + x2 = 0 + 6.25 0.6875x + x2 = 0 + 6.25 Combine like terms: 0 + 6.25 = 6.25 0.6875x + x2 = 6.25 The x term is 0.6875x. Take half its coefficient (0.34375). Square it (0.1181640625) and add it to both sides. Add '0.1181640625' to each side of the equation. 0.6875x + 0.1181640625 + x2 = 6.25 + 0.1181640625 Reorder the terms: 0.1181640625 + 0.6875x + x2 = 6.25 + 0.1181640625 Combine like terms: 6.25 + 0.1181640625 = 6.3681640625 0.1181640625 + 0.6875x + x2 = 6.3681640625 Factor a perfect square on the left side: (x + 0.34375)(x + 0.34375) = 6.3681640625 Calculate the square root of the right side: 2.523522154 Break this problem into two subproblems by setting (x + 0.34375) equal to 2.523522154 and -2.523522154.Subproblem 1
x + 0.34375 = 2.523522154 Simplifying x + 0.34375 = 2.523522154 Reorder the terms: 0.34375 + x = 2.523522154 Solving 0.34375 + x = 2.523522154 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.34375' to each side of the equation. 0.34375 + -0.34375 + x = 2.523522154 + -0.34375 Combine like terms: 0.34375 + -0.34375 = 0.00000 0.00000 + x = 2.523522154 + -0.34375 x = 2.523522154 + -0.34375 Combine like terms: 2.523522154 + -0.34375 = 2.179772154 x = 2.179772154 Simplifying x = 2.179772154Subproblem 2
x + 0.34375 = -2.523522154 Simplifying x + 0.34375 = -2.523522154 Reorder the terms: 0.34375 + x = -2.523522154 Solving 0.34375 + x = -2.523522154 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.34375' to each side of the equation. 0.34375 + -0.34375 + x = -2.523522154 + -0.34375 Combine like terms: 0.34375 + -0.34375 = 0.00000 0.00000 + x = -2.523522154 + -0.34375 x = -2.523522154 + -0.34375 Combine like terms: -2.523522154 + -0.34375 = -2.867272154 x = -2.867272154 Simplifying x = -2.867272154Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.179772154, -2.867272154}
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