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Simplifying 2x + x(x + 3) = 31 Reorder the terms: 2x + x(3 + x) = 31 2x + (3 * x + x * x) = 31 2x + (3x + x2) = 31 Combine like terms: 2x + 3x = 5x 5x + x2 = 31 Solving 5x + x2 = 31 Solving for variable 'x'. Reorder the terms: -31 + 5x + x2 = 31 + -31 Combine like terms: 31 + -31 = 0 -31 + 5x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '31' to each side of the equation. -31 + 5x + 31 + x2 = 0 + 31 Reorder the terms: -31 + 31 + 5x + x2 = 0 + 31 Combine like terms: -31 + 31 = 0 0 + 5x + x2 = 0 + 31 5x + x2 = 0 + 31 Combine like terms: 0 + 31 = 31 5x + x2 = 31 The x term is 5x. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5x + 6.25 + x2 = 31 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 31 + 6.25 Combine like terms: 31 + 6.25 = 37.25 6.25 + 5x + x2 = 37.25 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 37.25 Calculate the square root of the right side: 6.103277808 Break this problem into two subproblems by setting (x + 2.5) equal to 6.103277808 and -6.103277808.Subproblem 1
x + 2.5 = 6.103277808 Simplifying x + 2.5 = 6.103277808 Reorder the terms: 2.5 + x = 6.103277808 Solving 2.5 + x = 6.103277808 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 6.103277808 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 6.103277808 + -2.5 x = 6.103277808 + -2.5 Combine like terms: 6.103277808 + -2.5 = 3.603277808 x = 3.603277808 Simplifying x = 3.603277808Subproblem 2
x + 2.5 = -6.103277808 Simplifying x + 2.5 = -6.103277808 Reorder the terms: 2.5 + x = -6.103277808 Solving 2.5 + x = -6.103277808 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -6.103277808 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -6.103277808 + -2.5 x = -6.103277808 + -2.5 Combine like terms: -6.103277808 + -2.5 = -8.603277808 x = -8.603277808 Simplifying x = -8.603277808Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.603277808, -8.603277808}
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