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Simplifying x2 + 26 = 299x Reorder the terms: 26 + x2 = 299x Solving 26 + x2 = 299x Solving for variable 'x'. Reorder the terms: 26 + -299x + x2 = 299x + -299x Combine like terms: 299x + -299x = 0 26 + -299x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-26' to each side of the equation. 26 + -299x + -26 + x2 = 0 + -26 Reorder the terms: 26 + -26 + -299x + x2 = 0 + -26 Combine like terms: 26 + -26 = 0 0 + -299x + x2 = 0 + -26 -299x + x2 = 0 + -26 Combine like terms: 0 + -26 = -26 -299x + x2 = -26 The x term is -299x. Take half its coefficient (-149.5). Square it (22350.25) and add it to both sides. Add '22350.25' to each side of the equation. -299x + 22350.25 + x2 = -26 + 22350.25 Reorder the terms: 22350.25 + -299x + x2 = -26 + 22350.25 Combine like terms: -26 + 22350.25 = 22324.25 22350.25 + -299x + x2 = 22324.25 Factor a perfect square on the left side: (x + -149.5)(x + -149.5) = 22324.25 Calculate the square root of the right side: 149.413018174 Break this problem into two subproblems by setting (x + -149.5) equal to 149.413018174 and -149.413018174.Subproblem 1
x + -149.5 = 149.413018174 Simplifying x + -149.5 = 149.413018174 Reorder the terms: -149.5 + x = 149.413018174 Solving -149.5 + x = 149.413018174 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '149.5' to each side of the equation. -149.5 + 149.5 + x = 149.413018174 + 149.5 Combine like terms: -149.5 + 149.5 = 0.0 0.0 + x = 149.413018174 + 149.5 x = 149.413018174 + 149.5 Combine like terms: 149.413018174 + 149.5 = 298.913018174 x = 298.913018174 Simplifying x = 298.913018174Subproblem 2
x + -149.5 = -149.413018174 Simplifying x + -149.5 = -149.413018174 Reorder the terms: -149.5 + x = -149.413018174 Solving -149.5 + x = -149.413018174 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '149.5' to each side of the equation. -149.5 + 149.5 + x = -149.413018174 + 149.5 Combine like terms: -149.5 + 149.5 = 0.0 0.0 + x = -149.413018174 + 149.5 x = -149.413018174 + 149.5 Combine like terms: -149.413018174 + 149.5 = 0.086981826 x = 0.086981826 Simplifying x = 0.086981826Solution
The solution to the problem is based on the solutions from the subproblems. x = {298.913018174, 0.086981826}
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