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Simplifying x2 + -10 + x + -98 = 180 Reorder the terms: -10 + -98 + x + x2 = 180 Combine like terms: -10 + -98 = -108 -108 + x + x2 = 180 Solving -108 + x + x2 = 180 Solving for variable 'x'. Reorder the terms: -108 + -180 + x + x2 = 180 + -180 Combine like terms: -108 + -180 = -288 -288 + x + x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -288 + x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '288' to each side of the equation. -288 + x + 288 + x2 = 0 + 288 Reorder the terms: -288 + 288 + x + x2 = 0 + 288 Combine like terms: -288 + 288 = 0 0 + x + x2 = 0 + 288 x + x2 = 0 + 288 Combine like terms: 0 + 288 = 288 x + x2 = 288 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 = 288 + 0.25 Reorder the terms: 0.25 + x + x2 = 288 + 0.25 Combine like terms: 288 + 0.25 = 288.25 0.25 + x + x2 = 288.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 288.25 Calculate the square root of the right side: 16.977926846 Break this problem into two subproblems by setting (x + 0.5) equal to 16.977926846 and -16.977926846.Subproblem 1
x + 0.5 = 16.977926846 Simplifying x + 0.5 = 16.977926846 Reorder the terms: 0.5 + x = 16.977926846 Solving 0.5 + x = 16.977926846 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 = 16.977926846 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 16.977926846 + -0.5 x = 16.977926846 + -0.5 Combine like terms: 16.977926846 + -0.5 = 16.477926846 x = 16.477926846 Simplifying x = 16.477926846Subproblem 2
x + 0.5 = -16.977926846 Simplifying x + 0.5 = -16.977926846 Reorder the terms: 0.5 + x = -16.977926846 Solving 0.5 + x = -16.977926846 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 = -16.977926846 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -16.977926846 + -0.5 x = -16.977926846 + -0.5 Combine like terms: -16.977926846 + -0.5 = -17.477926846 x = -17.477926846 Simplifying x = -17.477926846Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.477926846, -17.477926846}
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