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Simplifying 4x + -33 + x(x + 12) = 806 Reorder the terms: 4x + -33 + x(12 + x) = 806 4x + -33 + (12 * x + x * x) = 806 4x + -33 + (12x + x2) = 806 Reorder the terms: -33 + 4x + 12x + x2 = 806 Combine like terms: 4x + 12x = 16x -33 + 16x + x2 = 806 Solving -33 + 16x + x2 = 806 Solving for variable 'x'. Reorder the terms: -33 + -806 + 16x + x2 = 806 + -806 Combine like terms: -33 + -806 = -839 -839 + 16x + x2 = 806 + -806 Combine like terms: 806 + -806 = 0 -839 + 16x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '839' to each side of the equation. -839 + 16x + 839 + x2 = 0 + 839 Reorder the terms: -839 + 839 + 16x + x2 = 0 + 839 Combine like terms: -839 + 839 = 0 0 + 16x + x2 = 0 + 839 16x + x2 = 0 + 839 Combine like terms: 0 + 839 = 839 16x + x2 = 839 The x term is 16x. Take half its coefficient (8). Square it (64) and add it to both sides. Add '64' to each side of the equation. 16x + 64 + x2 = 839 + 64 Reorder the terms: 64 + 16x + x2 = 839 + 64 Combine like terms: 839 + 64 = 903 64 + 16x + x2 = 903 Factor a perfect square on the left side: (x + 8)(x + 8) = 903 Calculate the square root of the right side: 30.049958403 Break this problem into two subproblems by setting (x + 8) equal to 30.049958403 and -30.049958403.Subproblem 1
x + 8 = 30.049958403 Simplifying x + 8 = 30.049958403 Reorder the terms: 8 + x = 30.049958403 Solving 8 + x = 30.049958403 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + x = 30.049958403 + -8 Combine like terms: 8 + -8 = 0 0 + x = 30.049958403 + -8 x = 30.049958403 + -8 Combine like terms: 30.049958403 + -8 = 22.049958403 x = 22.049958403 Simplifying x = 22.049958403Subproblem 2
x + 8 = -30.049958403 Simplifying x + 8 = -30.049958403 Reorder the terms: 8 + x = -30.049958403 Solving 8 + x = -30.049958403 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + x = -30.049958403 + -8 Combine like terms: 8 + -8 = 0 0 + x = -30.049958403 + -8 x = -30.049958403 + -8 Combine like terms: -30.049958403 + -8 = -38.049958403 x = -38.049958403 Simplifying x = -38.049958403Solution
The solution to the problem is based on the solutions from the subproblems. x = {22.049958403, -38.049958403}
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