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Simplifying x2 + 1.67x + -125.25 = 0 Reorder the terms: -125.25 + 1.67x + x2 = 0 Solving -125.25 + 1.67x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '125.25' to each side of the equation. -125.25 + 1.67x + 125.25 + x2 = 0 + 125.25 Reorder the terms: -125.25 + 125.25 + 1.67x + x2 = 0 + 125.25 Combine like terms: -125.25 + 125.25 = 0.00 0.00 + 1.67x + x2 = 0 + 125.25 1.67x + x2 = 0 + 125.25 Combine like terms: 0 + 125.25 = 125.25 1.67x + x2 = 125.25 The x term is 1.67x. Take half its coefficient (0.835). Square it (0.697225) and add it to both sides. Add '0.697225' to each side of the equation. 1.67x + 0.697225 + x2 = 125.25 + 0.697225 Reorder the terms: 0.697225 + 1.67x + x2 = 125.25 + 0.697225 Combine like terms: 125.25 + 0.697225 = 125.947225 0.697225 + 1.67x + x2 = 125.947225 Factor a perfect square on the left side: (x + 0.835)(x + 0.835) = 125.947225 Calculate the square root of the right side: 11.222621129 Break this problem into two subproblems by setting (x + 0.835) equal to 11.222621129 and -11.222621129.Subproblem 1
x + 0.835 = 11.222621129 Simplifying x + 0.835 = 11.222621129 Reorder the terms: 0.835 + x = 11.222621129 Solving 0.835 + x = 11.222621129 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.835' to each side of the equation. 0.835 + -0.835 + x = 11.222621129 + -0.835 Combine like terms: 0.835 + -0.835 = 0.000 0.000 + x = 11.222621129 + -0.835 x = 11.222621129 + -0.835 Combine like terms: 11.222621129 + -0.835 = 10.387621129 x = 10.387621129 Simplifying x = 10.387621129Subproblem 2
x + 0.835 = -11.222621129 Simplifying x + 0.835 = -11.222621129 Reorder the terms: 0.835 + x = -11.222621129 Solving 0.835 + x = -11.222621129 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.835' to each side of the equation. 0.835 + -0.835 + x = -11.222621129 + -0.835 Combine like terms: 0.835 + -0.835 = 0.000 0.000 + x = -11.222621129 + -0.835 x = -11.222621129 + -0.835 Combine like terms: -11.222621129 + -0.835 = -12.057621129 x = -12.057621129 Simplifying x = -12.057621129Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.387621129, -12.057621129}
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