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Simplifying -16x2 + -8x = 3x + -10 Reorder the terms: -8x + -16x2 = 3x + -10 Reorder the terms: -8x + -16x2 = -10 + 3x Solving -8x + -16x2 = -10 + 3x Solving for variable 'x'. Reorder the terms: 10 + -8x + -3x + -16x2 = -10 + 3x + 10 + -3x Combine like terms: -8x + -3x = -11x 10 + -11x + -16x2 = -10 + 3x + 10 + -3x Reorder the terms: 10 + -11x + -16x2 = -10 + 10 + 3x + -3x Combine like terms: -10 + 10 = 0 10 + -11x + -16x2 = 0 + 3x + -3x 10 + -11x + -16x2 = 3x + -3x Combine like terms: 3x + -3x = 0 10 + -11x + -16x2 = 0 Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. -0.625 + 0.6875x + x2 = 0 Move the constant term to the right: Add '0.625' to each side of the equation. -0.625 + 0.6875x + 0.625 + x2 = 0 + 0.625 Reorder the terms: -0.625 + 0.625 + 0.6875x + x2 = 0 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + 0.6875x + x2 = 0 + 0.625 0.6875x + x2 = 0 + 0.625 Combine like terms: 0 + 0.625 = 0.625 0.6875x + x2 = 0.625 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 = 0.625 + 0.1181640625 Reorder the terms: 0.1181640625 + 0.6875x + x2 = 0.625 + 0.1181640625 Combine like terms: 0.625 + 0.1181640625 = 0.7431640625 0.1181640625 + 0.6875x + x2 = 0.7431640625 Factor a perfect square on the left side: (x + 0.34375)(x + 0.34375) = 0.7431640625 Calculate the square root of the right side: 0.862069639 Break this problem into two subproblems by setting (x + 0.34375) equal to 0.862069639 and -0.862069639.Subproblem 1
x + 0.34375 = 0.862069639 Simplifying x + 0.34375 = 0.862069639 Reorder the terms: 0.34375 + x = 0.862069639 Solving 0.34375 + x = 0.862069639 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 = 0.862069639 + -0.34375 Combine like terms: 0.34375 + -0.34375 = 0.00000 0.00000 + x = 0.862069639 + -0.34375 x = 0.862069639 + -0.34375 Combine like terms: 0.862069639 + -0.34375 = 0.518319639 x = 0.518319639 Simplifying x = 0.518319639Subproblem 2
x + 0.34375 = -0.862069639 Simplifying x + 0.34375 = -0.862069639 Reorder the terms: 0.34375 + x = -0.862069639 Solving 0.34375 + x = -0.862069639 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 = -0.862069639 + -0.34375 Combine like terms: 0.34375 + -0.34375 = 0.00000 0.00000 + x = -0.862069639 + -0.34375 x = -0.862069639 + -0.34375 Combine like terms: -0.862069639 + -0.34375 = -1.205819639 x = -1.205819639 Simplifying x = -1.205819639Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.518319639, -1.205819639}
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