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Simplifying -16x2 + 43x + 24 = 0 Reorder the terms: 24 + 43x + -16x2 = 0 Solving 24 + 43x + -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'. -1.5 + -2.6875x + x2 = 0 Move the constant term to the right: Add '1.5' to each side of the equation. -1.5 + -2.6875x + 1.5 + x2 = 0 + 1.5 Reorder the terms: -1.5 + 1.5 + -2.6875x + x2 = 0 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + -2.6875x + x2 = 0 + 1.5 -2.6875x + x2 = 0 + 1.5 Combine like terms: 0 + 1.5 = 1.5 -2.6875x + x2 = 1.5 The x term is -2.6875x. Take half its coefficient (-1.34375). Square it (1.805664063) and add it to both sides. Add '1.805664063' to each side of the equation. -2.6875x + 1.805664063 + x2 = 1.5 + 1.805664063 Reorder the terms: 1.805664063 + -2.6875x + x2 = 1.5 + 1.805664063 Combine like terms: 1.5 + 1.805664063 = 3.305664063 1.805664063 + -2.6875x + x2 = 3.305664063 Factor a perfect square on the left side: (x + -1.34375)(x + -1.34375) = 3.305664063 Calculate the square root of the right side: 1.818148526 Break this problem into two subproblems by setting (x + -1.34375) equal to 1.818148526 and -1.818148526.Subproblem 1
x + -1.34375 = 1.818148526 Simplifying x + -1.34375 = 1.818148526 Reorder the terms: -1.34375 + x = 1.818148526 Solving -1.34375 + x = 1.818148526 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.34375' to each side of the equation. -1.34375 + 1.34375 + x = 1.818148526 + 1.34375 Combine like terms: -1.34375 + 1.34375 = 0.00000 0.00000 + x = 1.818148526 + 1.34375 x = 1.818148526 + 1.34375 Combine like terms: 1.818148526 + 1.34375 = 3.161898526 x = 3.161898526 Simplifying x = 3.161898526Subproblem 2
x + -1.34375 = -1.818148526 Simplifying x + -1.34375 = -1.818148526 Reorder the terms: -1.34375 + x = -1.818148526 Solving -1.34375 + x = -1.818148526 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.34375' to each side of the equation. -1.34375 + 1.34375 + x = -1.818148526 + 1.34375 Combine like terms: -1.34375 + 1.34375 = 0.00000 0.00000 + x = -1.818148526 + 1.34375 x = -1.818148526 + 1.34375 Combine like terms: -1.818148526 + 1.34375 = -0.474398526 x = -0.474398526 Simplifying x = -0.474398526Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.161898526, -0.474398526}
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