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Simplifying x(x + 4) + 2(x + 3) = 5 Reorder the terms: x(4 + x) + 2(x + 3) = 5 (4 * x + x * x) + 2(x + 3) = 5 (4x + x2) + 2(x + 3) = 5 Reorder the terms: 4x + x2 + 2(3 + x) = 5 4x + x2 + (3 * 2 + x * 2) = 5 4x + x2 + (6 + 2x) = 5 Reorder the terms: 6 + 4x + 2x + x2 = 5 Combine like terms: 4x + 2x = 6x 6 + 6x + x2 = 5 Solving 6 + 6x + x2 = 5 Solving for variable 'x'. Reorder the terms: 6 + -5 + 6x + x2 = 5 + -5 Combine like terms: 6 + -5 = 1 1 + 6x + x2 = 5 + -5 Combine like terms: 5 + -5 = 0 1 + 6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-1' to each side of the equation. 1 + 6x + -1 + x2 = 0 + -1 Reorder the terms: 1 + -1 + 6x + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 6x + x2 = 0 + -1 6x + x2 = 0 + -1 Combine like terms: 0 + -1 = -1 6x + x2 = -1 The x term is 6x. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x + 9 + x2 = -1 + 9 Reorder the terms: 9 + 6x + x2 = -1 + 9 Combine like terms: -1 + 9 = 8 9 + 6x + x2 = 8 Factor a perfect square on the left side: (x + 3)(x + 3) = 8 Calculate the square root of the right side: 2.828427125 Break this problem into two subproblems by setting (x + 3) equal to 2.828427125 and -2.828427125.Subproblem 1
x + 3 = 2.828427125 Simplifying x + 3 = 2.828427125 Reorder the terms: 3 + x = 2.828427125 Solving 3 + x = 2.828427125 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 2.828427125 + -3 Combine like terms: 3 + -3 = 0 0 + x = 2.828427125 + -3 x = 2.828427125 + -3 Combine like terms: 2.828427125 + -3 = -0.171572875 x = -0.171572875 Simplifying x = -0.171572875Subproblem 2
x + 3 = -2.828427125 Simplifying x + 3 = -2.828427125 Reorder the terms: 3 + x = -2.828427125 Solving 3 + x = -2.828427125 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -2.828427125 + -3 Combine like terms: 3 + -3 = 0 0 + x = -2.828427125 + -3 x = -2.828427125 + -3 Combine like terms: -2.828427125 + -3 = -5.828427125 x = -5.828427125 Simplifying x = -5.828427125Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.171572875, -5.828427125}
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