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Simplifying (x + -3)(x + 1) = 3600 Reorder the terms: (-3 + x)(x + 1) = 3600 Reorder the terms: (-3 + x)(1 + x) = 3600 Multiply (-3 + x) * (1 + x) (-3(1 + x) + x(1 + x)) = 3600 ((1 * -3 + x * -3) + x(1 + x)) = 3600 ((-3 + -3x) + x(1 + x)) = 3600 (-3 + -3x + (1 * x + x * x)) = 3600 (-3 + -3x + (1x + x2)) = 3600 Combine like terms: -3x + 1x = -2x (-3 + -2x + x2) = 3600 Solving -3 + -2x + x2 = 3600 Solving for variable 'x'. Reorder the terms: -3 + -3600 + -2x + x2 = 3600 + -3600 Combine like terms: -3 + -3600 = -3603 -3603 + -2x + x2 = 3600 + -3600 Combine like terms: 3600 + -3600 = 0 -3603 + -2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '3603' to each side of the equation. -3603 + -2x + 3603 + x2 = 0 + 3603 Reorder the terms: -3603 + 3603 + -2x + x2 = 0 + 3603 Combine like terms: -3603 + 3603 = 0 0 + -2x + x2 = 0 + 3603 -2x + x2 = 0 + 3603 Combine like terms: 0 + 3603 = 3603 -2x + x2 = 3603 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 3603 + 1 Reorder the terms: 1 + -2x + x2 = 3603 + 1 Combine like terms: 3603 + 1 = 3604 1 + -2x + x2 = 3604 Factor a perfect square on the left side: (x + -1)(x + -1) = 3604 Calculate the square root of the right side: 60.033324079 Break this problem into two subproblems by setting (x + -1) equal to 60.033324079 and -60.033324079.Subproblem 1
x + -1 = 60.033324079 Simplifying x + -1 = 60.033324079 Reorder the terms: -1 + x = 60.033324079 Solving -1 + x = 60.033324079 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 60.033324079 + 1 Combine like terms: -1 + 1 = 0 0 + x = 60.033324079 + 1 x = 60.033324079 + 1 Combine like terms: 60.033324079 + 1 = 61.033324079 x = 61.033324079 Simplifying x = 61.033324079Subproblem 2
x + -1 = -60.033324079 Simplifying x + -1 = -60.033324079 Reorder the terms: -1 + x = -60.033324079 Solving -1 + x = -60.033324079 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -60.033324079 + 1 Combine like terms: -1 + 1 = 0 0 + x = -60.033324079 + 1 x = -60.033324079 + 1 Combine like terms: -60.033324079 + 1 = -59.033324079 x = -59.033324079 Simplifying x = -59.033324079Solution
The solution to the problem is based on the solutions from the subproblems. x = {61.033324079, -59.033324079}
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