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Simplifying x(x + 5) = 98 Reorder the terms: x(5 + x) = 98 (5 * x + x * x) = 98 (5x + x2) = 98 Solving 5x + x2 = 98 Solving for variable 'x'. Reorder the terms: -98 + 5x + x2 = 98 + -98 Combine like terms: 98 + -98 = 0 -98 + 5x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '98' to each side of the equation. -98 + 5x + 98 + x2 = 0 + 98 Reorder the terms: -98 + 98 + 5x + x2 = 0 + 98 Combine like terms: -98 + 98 = 0 0 + 5x + x2 = 0 + 98 5x + x2 = 0 + 98 Combine like terms: 0 + 98 = 98 5x + x2 = 98 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 = 98 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 98 + 6.25 Combine like terms: 98 + 6.25 = 104.25 6.25 + 5x + x2 = 104.25 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 104.25 Calculate the square root of the right side: 10.210288928 Break this problem into two subproblems by setting (x + 2.5) equal to 10.210288928 and -10.210288928.Subproblem 1
x + 2.5 = 10.210288928 Simplifying x + 2.5 = 10.210288928 Reorder the terms: 2.5 + x = 10.210288928 Solving 2.5 + x = 10.210288928 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 = 10.210288928 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 10.210288928 + -2.5 x = 10.210288928 + -2.5 Combine like terms: 10.210288928 + -2.5 = 7.710288928 x = 7.710288928 Simplifying x = 7.710288928Subproblem 2
x + 2.5 = -10.210288928 Simplifying x + 2.5 = -10.210288928 Reorder the terms: 2.5 + x = -10.210288928 Solving 2.5 + x = -10.210288928 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 = -10.210288928 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -10.210288928 + -2.5 x = -10.210288928 + -2.5 Combine like terms: -10.210288928 + -2.5 = -12.710288928 x = -12.710288928 Simplifying x = -12.710288928Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.710288928, -12.710288928}
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