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Simplifying x(x + 3) + (x + 2) + (x + 7) = 40 Reorder the terms: x(3 + x) + (x + 2) + (x + 7) = 40 (3 * x + x * x) + (x + 2) + (x + 7) = 40 (3x + x2) + (x + 2) + (x + 7) = 40 Reorder the terms: 3x + x2 + (2 + x) + (x + 7) = 40 Remove parenthesis around (2 + x) 3x + x2 + 2 + x + (x + 7) = 40 Reorder the terms: 3x + x2 + 2 + x + (7 + x) = 40 Remove parenthesis around (7 + x) 3x + x2 + 2 + x + 7 + x = 40 Reorder the terms: 2 + 7 + 3x + x + x + x2 = 40 Combine like terms: 2 + 7 = 9 9 + 3x + x + x + x2 = 40 Combine like terms: 3x + x = 4x 9 + 4x + x + x2 = 40 Combine like terms: 4x + x = 5x 9 + 5x + x2 = 40 Solving 9 + 5x + x2 = 40 Solving for variable 'x'. Reorder the terms: 9 + -40 + 5x + x2 = 40 + -40 Combine like terms: 9 + -40 = -31 -31 + 5x + x2 = 40 + -40 Combine like terms: 40 + -40 = 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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