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Simplifying (x + 55) * x = 90 Reorder the terms: (55 + x) * x = 90 Reorder the terms for easier multiplication: x(55 + x) = 90 (55 * x + x * x) = 90 (55x + x2) = 90 Solving 55x + x2 = 90 Solving for variable 'x'. Reorder the terms: -90 + 55x + x2 = 90 + -90 Combine like terms: 90 + -90 = 0 -90 + 55x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '90' to each side of the equation. -90 + 55x + 90 + x2 = 0 + 90 Reorder the terms: -90 + 90 + 55x + x2 = 0 + 90 Combine like terms: -90 + 90 = 0 0 + 55x + x2 = 0 + 90 55x + x2 = 0 + 90 Combine like terms: 0 + 90 = 90 55x + x2 = 90 The x term is 55x. Take half its coefficient (27.5). Square it (756.25) and add it to both sides. Add '756.25' to each side of the equation. 55x + 756.25 + x2 = 90 + 756.25 Reorder the terms: 756.25 + 55x + x2 = 90 + 756.25 Combine like terms: 90 + 756.25 = 846.25 756.25 + 55x + x2 = 846.25 Factor a perfect square on the left side: (x + 27.5)(x + 27.5) = 846.25 Calculate the square root of the right side: 29.090376416 Break this problem into two subproblems by setting (x + 27.5) equal to 29.090376416 and -29.090376416.Subproblem 1
x + 27.5 = 29.090376416 Simplifying x + 27.5 = 29.090376416 Reorder the terms: 27.5 + x = 29.090376416 Solving 27.5 + x = 29.090376416 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-27.5' to each side of the equation. 27.5 + -27.5 + x = 29.090376416 + -27.5 Combine like terms: 27.5 + -27.5 = 0.0 0.0 + x = 29.090376416 + -27.5 x = 29.090376416 + -27.5 Combine like terms: 29.090376416 + -27.5 = 1.590376416 x = 1.590376416 Simplifying x = 1.590376416Subproblem 2
x + 27.5 = -29.090376416 Simplifying x + 27.5 = -29.090376416 Reorder the terms: 27.5 + x = -29.090376416 Solving 27.5 + x = -29.090376416 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-27.5' to each side of the equation. 27.5 + -27.5 + x = -29.090376416 + -27.5 Combine like terms: 27.5 + -27.5 = 0.0 0.0 + x = -29.090376416 + -27.5 x = -29.090376416 + -27.5 Combine like terms: -29.090376416 + -27.5 = -56.590376416 x = -56.590376416 Simplifying x = -56.590376416Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.590376416, -56.590376416}
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