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Simplifying -16x2 + -11x + 170 = 0 Reorder the terms: 170 + -11x + -16x2 = 0 Solving 170 + -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'. -10.625 + 0.6875x + x2 = 0 Move the constant term to the right: Add '10.625' to each side of the equation. -10.625 + 0.6875x + 10.625 + x2 = 0 + 10.625 Reorder the terms: -10.625 + 10.625 + 0.6875x + x2 = 0 + 10.625 Combine like terms: -10.625 + 10.625 = 0.000 0.000 + 0.6875x + x2 = 0 + 10.625 0.6875x + x2 = 0 + 10.625 Combine like terms: 0 + 10.625 = 10.625 0.6875x + x2 = 10.625 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 = 10.625 + 0.1181640625 Reorder the terms: 0.1181640625 + 0.6875x + x2 = 10.625 + 0.1181640625 Combine like terms: 10.625 + 0.1181640625 = 10.7431640625 0.1181640625 + 0.6875x + x2 = 10.7431640625 Factor a perfect square on the left side: (x + 0.34375)(x + 0.34375) = 10.7431640625 Calculate the square root of the right side: 3.277676626 Break this problem into two subproblems by setting (x + 0.34375) equal to 3.277676626 and -3.277676626.Subproblem 1
x + 0.34375 = 3.277676626 Simplifying x + 0.34375 = 3.277676626 Reorder the terms: 0.34375 + x = 3.277676626 Solving 0.34375 + x = 3.277676626 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 = 3.277676626 + -0.34375 Combine like terms: 0.34375 + -0.34375 = 0.00000 0.00000 + x = 3.277676626 + -0.34375 x = 3.277676626 + -0.34375 Combine like terms: 3.277676626 + -0.34375 = 2.933926626 x = 2.933926626 Simplifying x = 2.933926626Subproblem 2
x + 0.34375 = -3.277676626 Simplifying x + 0.34375 = -3.277676626 Reorder the terms: 0.34375 + x = -3.277676626 Solving 0.34375 + x = -3.277676626 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 = -3.277676626 + -0.34375 Combine like terms: 0.34375 + -0.34375 = 0.00000 0.00000 + x = -3.277676626 + -0.34375 x = -3.277676626 + -0.34375 Combine like terms: -3.277676626 + -0.34375 = -3.621426626 x = -3.621426626 Simplifying x = -3.621426626Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.933926626, -3.621426626}
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