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Simplifying (x + -0.5)(x + 9) = 2.5 Reorder the terms: (-0.5 + x)(x + 9) = 2.5 Reorder the terms: (-0.5 + x)(9 + x) = 2.5 Multiply (-0.5 + x) * (9 + x) (-0.5(9 + x) + x(9 + x)) = 2.5 ((9 * -0.5 + x * -0.5) + x(9 + x)) = 2.5 ((-4.5 + -0.5x) + x(9 + x)) = 2.5 (-4.5 + -0.5x + (9 * x + x * x)) = 2.5 (-4.5 + -0.5x + (9x + x2)) = 2.5 Combine like terms: -0.5x + 9x = 8.5x (-4.5 + 8.5x + x2) = 2.5 Solving -4.5 + 8.5x + x2 = 2.5 Solving for variable 'x'. Reorder the terms: -4.5 + -2.5 + 8.5x + x2 = 2.5 + -2.5 Combine like terms: -4.5 + -2.5 = -7 -7 + 8.5x + x2 = 2.5 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 -7 + 8.5x + x2 = 0.0 Begin completing the square. Move the constant term to the right: Add '7' to each side of the equation. -7 + 8.5x + 7 + x2 = 0.0 + 7 Reorder the terms: -7 + 7 + 8.5x + x2 = 0.0 + 7 Combine like terms: -7 + 7 = 0 0 + 8.5x + x2 = 0.0 + 7 8.5x + x2 = 0.0 + 7 Combine like terms: 0.0 + 7 = 7 8.5x + x2 = 7 The x term is 8.5x. Take half its coefficient (4.25). Square it (18.0625) and add it to both sides. Add '18.0625' to each side of the equation. 8.5x + 18.0625 + x2 = 7 + 18.0625 Reorder the terms: 18.0625 + 8.5x + x2 = 7 + 18.0625 Combine like terms: 7 + 18.0625 = 25.0625 18.0625 + 8.5x + x2 = 25.0625 Factor a perfect square on the left side: (x + 4.25)(x + 4.25) = 25.0625 Calculate the square root of the right side: 5.006246099 Break this problem into two subproblems by setting (x + 4.25) equal to 5.006246099 and -5.006246099.Subproblem 1
x + 4.25 = 5.006246099 Simplifying x + 4.25 = 5.006246099 Reorder the terms: 4.25 + x = 5.006246099 Solving 4.25 + x = 5.006246099 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.25' to each side of the equation. 4.25 + -4.25 + x = 5.006246099 + -4.25 Combine like terms: 4.25 + -4.25 = 0.00 0.00 + x = 5.006246099 + -4.25 x = 5.006246099 + -4.25 Combine like terms: 5.006246099 + -4.25 = 0.756246099 x = 0.756246099 Simplifying x = 0.756246099Subproblem 2
x + 4.25 = -5.006246099 Simplifying x + 4.25 = -5.006246099 Reorder the terms: 4.25 + x = -5.006246099 Solving 4.25 + x = -5.006246099 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.25' to each side of the equation. 4.25 + -4.25 + x = -5.006246099 + -4.25 Combine like terms: 4.25 + -4.25 = 0.00 0.00 + x = -5.006246099 + -4.25 x = -5.006246099 + -4.25 Combine like terms: -5.006246099 + -4.25 = -9.256246099 x = -9.256246099 Simplifying x = -9.256246099Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.756246099, -9.256246099}
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