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Simplifying (x + -3)(x + 17) = 1 Reorder the terms: (-3 + x)(x + 17) = 1 Reorder the terms: (-3 + x)(17 + x) = 1 Multiply (-3 + x) * (17 + x) (-3(17 + x) + x(17 + x)) = 1 ((17 * -3 + x * -3) + x(17 + x)) = 1 ((-51 + -3x) + x(17 + x)) = 1 (-51 + -3x + (17 * x + x * x)) = 1 (-51 + -3x + (17x + x2)) = 1 Combine like terms: -3x + 17x = 14x (-51 + 14x + x2) = 1 Solving -51 + 14x + x2 = 1 Solving for variable 'x'. Reorder the terms: -51 + -1 + 14x + x2 = 1 + -1 Combine like terms: -51 + -1 = -52 -52 + 14x + x2 = 1 + -1 Combine like terms: 1 + -1 = 0 -52 + 14x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '52' to each side of the equation. -52 + 14x + 52 + x2 = 0 + 52 Reorder the terms: -52 + 52 + 14x + x2 = 0 + 52 Combine like terms: -52 + 52 = 0 0 + 14x + x2 = 0 + 52 14x + x2 = 0 + 52 Combine like terms: 0 + 52 = 52 14x + x2 = 52 The x term is 14x. Take half its coefficient (7). Square it (49) and add it to both sides. Add '49' to each side of the equation. 14x + 49 + x2 = 52 + 49 Reorder the terms: 49 + 14x + x2 = 52 + 49 Combine like terms: 52 + 49 = 101 49 + 14x + x2 = 101 Factor a perfect square on the left side: (x + 7)(x + 7) = 101 Calculate the square root of the right side: 10.049875621 Break this problem into two subproblems by setting (x + 7) equal to 10.049875621 and -10.049875621.Subproblem 1
x + 7 = 10.049875621 Simplifying x + 7 = 10.049875621 Reorder the terms: 7 + x = 10.049875621 Solving 7 + x = 10.049875621 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + x = 10.049875621 + -7 Combine like terms: 7 + -7 = 0 0 + x = 10.049875621 + -7 x = 10.049875621 + -7 Combine like terms: 10.049875621 + -7 = 3.049875621 x = 3.049875621 Simplifying x = 3.049875621Subproblem 2
x + 7 = -10.049875621 Simplifying x + 7 = -10.049875621 Reorder the terms: 7 + x = -10.049875621 Solving 7 + x = -10.049875621 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + x = -10.049875621 + -7 Combine like terms: 7 + -7 = 0 0 + x = -10.049875621 + -7 x = -10.049875621 + -7 Combine like terms: -10.049875621 + -7 = -17.049875621 x = -17.049875621 Simplifying x = -17.049875621Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.049875621, -17.049875621}
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