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Simplifying 4x(3 + x) = 16 + x (3 * 4x + x * 4x) = 16 + x (12x + 4x2) = 16 + x Solving 12x + 4x2 = 16 + x Solving for variable 'x'. Reorder the terms: -16 + 12x + -1x + 4x2 = 16 + x + -16 + -1x Combine like terms: 12x + -1x = 11x -16 + 11x + 4x2 = 16 + x + -16 + -1x Reorder the terms: -16 + 11x + 4x2 = 16 + -16 + x + -1x Combine like terms: 16 + -16 = 0 -16 + 11x + 4x2 = 0 + x + -1x -16 + 11x + 4x2 = x + -1x Combine like terms: x + -1x = 0 -16 + 11x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -4 + 2.75x + x2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + 2.75x + 4 + x2 = 0 + 4 Reorder the terms: -4 + 4 + 2.75x + x2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 2.75x + x2 = 0 + 4 2.75x + x2 = 0 + 4 Combine like terms: 0 + 4 = 4 2.75x + x2 = 4 The x term is 2.75x. Take half its coefficient (1.375). Square it (1.890625) and add it to both sides. Add '1.890625' to each side of the equation. 2.75x + 1.890625 + x2 = 4 + 1.890625 Reorder the terms: 1.890625 + 2.75x + x2 = 4 + 1.890625 Combine like terms: 4 + 1.890625 = 5.890625 1.890625 + 2.75x + x2 = 5.890625 Factor a perfect square on the left side: (x + 1.375)(x + 1.375) = 5.890625 Calculate the square root of the right side: 2.42706098 Break this problem into two subproblems by setting (x + 1.375) equal to 2.42706098 and -2.42706098.Subproblem 1
x + 1.375 = 2.42706098 Simplifying x + 1.375 = 2.42706098 Reorder the terms: 1.375 + x = 2.42706098 Solving 1.375 + x = 2.42706098 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.375' to each side of the equation. 1.375 + -1.375 + x = 2.42706098 + -1.375 Combine like terms: 1.375 + -1.375 = 0.000 0.000 + x = 2.42706098 + -1.375 x = 2.42706098 + -1.375 Combine like terms: 2.42706098 + -1.375 = 1.05206098 x = 1.05206098 Simplifying x = 1.05206098Subproblem 2
x + 1.375 = -2.42706098 Simplifying x + 1.375 = -2.42706098 Reorder the terms: 1.375 + x = -2.42706098 Solving 1.375 + x = -2.42706098 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.375' to each side of the equation. 1.375 + -1.375 + x = -2.42706098 + -1.375 Combine like terms: 1.375 + -1.375 = 0.000 0.000 + x = -2.42706098 + -1.375 x = -2.42706098 + -1.375 Combine like terms: -2.42706098 + -1.375 = -3.80206098 x = -3.80206098 Simplifying x = -3.80206098Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.05206098, -3.80206098}
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