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Simplifying x(x + 5) = 2 + 55 Reorder the terms: x(5 + x) = 2 + 55 (5 * x + x * x) = 2 + 55 (5x + x2) = 2 + 55 Combine like terms: 2 + 55 = 57 5x + x2 = 57 Solving 5x + x2 = 57 Solving for variable 'x'. Reorder the terms: -57 + 5x + x2 = 57 + -57 Combine like terms: 57 + -57 = 0 -57 + 5x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '57' to each side of the equation. -57 + 5x + 57 + x2 = 0 + 57 Reorder the terms: -57 + 57 + 5x + x2 = 0 + 57 Combine like terms: -57 + 57 = 0 0 + 5x + x2 = 0 + 57 5x + x2 = 0 + 57 Combine like terms: 0 + 57 = 57 5x + x2 = 57 The x term is 5x. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5x + 6.25 + x2 = 57 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 57 + 6.25 Combine like terms: 57 + 6.25 = 63.25 6.25 + 5x + x2 = 63.25 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 63.25 Calculate the square root of the right side: 7.95298686 Break this problem into two subproblems by setting (x + 2.5) equal to 7.95298686 and -7.95298686.Subproblem 1
x + 2.5 = 7.95298686 Simplifying x + 2.5 = 7.95298686 Reorder the terms: 2.5 + x = 7.95298686 Solving 2.5 + x = 7.95298686 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 7.95298686 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 7.95298686 + -2.5 x = 7.95298686 + -2.5 Combine like terms: 7.95298686 + -2.5 = 5.45298686 x = 5.45298686 Simplifying x = 5.45298686Subproblem 2
x + 2.5 = -7.95298686 Simplifying x + 2.5 = -7.95298686 Reorder the terms: 2.5 + x = -7.95298686 Solving 2.5 + x = -7.95298686 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -7.95298686 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -7.95298686 + -2.5 x = -7.95298686 + -2.5 Combine like terms: -7.95298686 + -2.5 = -10.45298686 x = -10.45298686 Simplifying x = -10.45298686Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.45298686, -10.45298686}
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