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Simplifying x2 + x = 98 Reorder the terms: x + x2 = 98 Solving x + x2 = 98 Solving for variable 'x'. Reorder the terms: -98 + x + x2 = 98 + -98 Combine like terms: 98 + -98 = 0 -98 + x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '98' to each side of the equation. -98 + x + 98 + x2 = 0 + 98 Reorder the terms: -98 + 98 + x + x2 = 0 + 98 Combine like terms: -98 + 98 = 0 0 + x + x2 = 0 + 98 x + x2 = 0 + 98 Combine like terms: 0 + 98 = 98 x + x2 = 98 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. x + 0.25 + x2 = 98 + 0.25 Reorder the terms: 0.25 + x + x2 = 98 + 0.25 Combine like terms: 98 + 0.25 = 98.25 0.25 + x + x2 = 98.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 98.25 Calculate the square root of the right side: 9.912113801 Break this problem into two subproblems by setting (x + 0.5) equal to 9.912113801 and -9.912113801.Subproblem 1
x + 0.5 = 9.912113801 Simplifying x + 0.5 = 9.912113801 Reorder the terms: 0.5 + x = 9.912113801 Solving 0.5 + x = 9.912113801 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 9.912113801 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 9.912113801 + -0.5 x = 9.912113801 + -0.5 Combine like terms: 9.912113801 + -0.5 = 9.412113801 x = 9.412113801 Simplifying x = 9.412113801Subproblem 2
x + 0.5 = -9.912113801 Simplifying x + 0.5 = -9.912113801 Reorder the terms: 0.5 + x = -9.912113801 Solving 0.5 + x = -9.912113801 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -9.912113801 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -9.912113801 + -0.5 x = -9.912113801 + -0.5 Combine like terms: -9.912113801 + -0.5 = -10.412113801 x = -10.412113801 Simplifying x = -10.412113801Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.412113801, -10.412113801}
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