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Simplifying x2 + -5x = 98 Reorder the terms: -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 = 12.710288928 x = 12.710288928 Simplifying x = 12.710288928Subproblem 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 = -7.710288928 x = -7.710288928 Simplifying x = -7.710288928Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.710288928, -7.710288928}
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