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Simplifying x2 + x + -303 = 0 Reorder the terms: -303 + x + x2 = 0 Solving -303 + x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '303' to each side of the equation. -303 + x + 303 + x2 = 0 + 303 Reorder the terms: -303 + 303 + x + x2 = 0 + 303 Combine like terms: -303 + 303 = 0 0 + x + x2 = 0 + 303 x + x2 = 0 + 303 Combine like terms: 0 + 303 = 303 x + x2 = 303 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 = 303 + 0.25 Reorder the terms: 0.25 + x + x2 = 303 + 0.25 Combine like terms: 303 + 0.25 = 303.25 0.25 + x + x2 = 303.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 303.25 Calculate the square root of the right side: 17.414074767 Break this problem into two subproblems by setting (x + 0.5) equal to 17.414074767 and -17.414074767.Subproblem 1
x + 0.5 = 17.414074767 Simplifying x + 0.5 = 17.414074767 Reorder the terms: 0.5 + x = 17.414074767 Solving 0.5 + x = 17.414074767 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 = 17.414074767 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 17.414074767 + -0.5 x = 17.414074767 + -0.5 Combine like terms: 17.414074767 + -0.5 = 16.914074767 x = 16.914074767 Simplifying x = 16.914074767Subproblem 2
x + 0.5 = -17.414074767 Simplifying x + 0.5 = -17.414074767 Reorder the terms: 0.5 + x = -17.414074767 Solving 0.5 + x = -17.414074767 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 = -17.414074767 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -17.414074767 + -0.5 x = -17.414074767 + -0.5 Combine like terms: -17.414074767 + -0.5 = -17.914074767 x = -17.914074767 Simplifying x = -17.914074767Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.914074767, -17.914074767}
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