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Simplifying -4x2 + -27x + 16 = 8x + 4 Reorder the terms: 16 + -27x + -4x2 = 8x + 4 Reorder the terms: 16 + -27x + -4x2 = 4 + 8x Solving 16 + -27x + -4x2 = 4 + 8x Solving for variable 'x'. Reorder the terms: 16 + -4 + -27x + -8x + -4x2 = 4 + 8x + -4 + -8x Combine like terms: 16 + -4 = 12 12 + -27x + -8x + -4x2 = 4 + 8x + -4 + -8x Combine like terms: -27x + -8x = -35x 12 + -35x + -4x2 = 4 + 8x + -4 + -8x Reorder the terms: 12 + -35x + -4x2 = 4 + -4 + 8x + -8x Combine like terms: 4 + -4 = 0 12 + -35x + -4x2 = 0 + 8x + -8x 12 + -35x + -4x2 = 8x + -8x Combine like terms: 8x + -8x = 0 12 + -35x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -3 + 8.75x + x2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + 8.75x + 3 + x2 = 0 + 3 Reorder the terms: -3 + 3 + 8.75x + x2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 8.75x + x2 = 0 + 3 8.75x + x2 = 0 + 3 Combine like terms: 0 + 3 = 3 8.75x + x2 = 3 The x term is 8.75x. Take half its coefficient (4.375). Square it (19.140625) and add it to both sides. Add '19.140625' to each side of the equation. 8.75x + 19.140625 + x2 = 3 + 19.140625 Reorder the terms: 19.140625 + 8.75x + x2 = 3 + 19.140625 Combine like terms: 3 + 19.140625 = 22.140625 19.140625 + 8.75x + x2 = 22.140625 Factor a perfect square on the left side: (x + 4.375)(x + 4.375) = 22.140625 Calculate the square root of the right side: 4.705382556 Break this problem into two subproblems by setting (x + 4.375) equal to 4.705382556 and -4.705382556.Subproblem 1
x + 4.375 = 4.705382556 Simplifying x + 4.375 = 4.705382556 Reorder the terms: 4.375 + x = 4.705382556 Solving 4.375 + x = 4.705382556 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.375' to each side of the equation. 4.375 + -4.375 + x = 4.705382556 + -4.375 Combine like terms: 4.375 + -4.375 = 0.000 0.000 + x = 4.705382556 + -4.375 x = 4.705382556 + -4.375 Combine like terms: 4.705382556 + -4.375 = 0.330382556 x = 0.330382556 Simplifying x = 0.330382556Subproblem 2
x + 4.375 = -4.705382556 Simplifying x + 4.375 = -4.705382556 Reorder the terms: 4.375 + x = -4.705382556 Solving 4.375 + x = -4.705382556 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.375' to each side of the equation. 4.375 + -4.375 + x = -4.705382556 + -4.375 Combine like terms: 4.375 + -4.375 = 0.000 0.000 + x = -4.705382556 + -4.375 x = -4.705382556 + -4.375 Combine like terms: -4.705382556 + -4.375 = -9.080382556 x = -9.080382556 Simplifying x = -9.080382556Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.330382556, -9.080382556}
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