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Simplifying (x + -9)(x + 5) = 45 Reorder the terms: (-9 + x)(x + 5) = 45 Reorder the terms: (-9 + x)(5 + x) = 45 Multiply (-9 + x) * (5 + x) (-9(5 + x) + x(5 + x)) = 45 ((5 * -9 + x * -9) + x(5 + x)) = 45 ((-45 + -9x) + x(5 + x)) = 45 (-45 + -9x + (5 * x + x * x)) = 45 (-45 + -9x + (5x + x2)) = 45 Combine like terms: -9x + 5x = -4x (-45 + -4x + x2) = 45 Solving -45 + -4x + x2 = 45 Solving for variable 'x'. Reorder the terms: -45 + -45 + -4x + x2 = 45 + -45 Combine like terms: -45 + -45 = -90 -90 + -4x + x2 = 45 + -45 Combine like terms: 45 + -45 = 0 -90 + -4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '90' to each side of the equation. -90 + -4x + 90 + x2 = 0 + 90 Reorder the terms: -90 + 90 + -4x + x2 = 0 + 90 Combine like terms: -90 + 90 = 0 0 + -4x + x2 = 0 + 90 -4x + x2 = 0 + 90 Combine like terms: 0 + 90 = 90 -4x + x2 = 90 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = 90 + 4 Reorder the terms: 4 + -4x + x2 = 90 + 4 Combine like terms: 90 + 4 = 94 4 + -4x + x2 = 94 Factor a perfect square on the left side: (x + -2)(x + -2) = 94 Calculate the square root of the right side: 9.695359715 Break this problem into two subproblems by setting (x + -2) equal to 9.695359715 and -9.695359715.Subproblem 1
x + -2 = 9.695359715 Simplifying x + -2 = 9.695359715 Reorder the terms: -2 + x = 9.695359715 Solving -2 + x = 9.695359715 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 9.695359715 + 2 Combine like terms: -2 + 2 = 0 0 + x = 9.695359715 + 2 x = 9.695359715 + 2 Combine like terms: 9.695359715 + 2 = 11.695359715 x = 11.695359715 Simplifying x = 11.695359715Subproblem 2
x + -2 = -9.695359715 Simplifying x + -2 = -9.695359715 Reorder the terms: -2 + x = -9.695359715 Solving -2 + x = -9.695359715 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -9.695359715 + 2 Combine like terms: -2 + 2 = 0 0 + x = -9.695359715 + 2 x = -9.695359715 + 2 Combine like terms: -9.695359715 + 2 = -7.695359715 x = -7.695359715 Simplifying x = -7.695359715Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.695359715, -7.695359715}
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