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Simplifying x2 + 11x + -10 = 180 Reorder the terms: -10 + 11x + x2 = 180 Solving -10 + 11x + x2 = 180 Solving for variable 'x'. Reorder the terms: -10 + -180 + 11x + x2 = 180 + -180 Combine like terms: -10 + -180 = -190 -190 + 11x + x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -190 + 11x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '190' to each side of the equation. -190 + 11x + 190 + x2 = 0 + 190 Reorder the terms: -190 + 190 + 11x + x2 = 0 + 190 Combine like terms: -190 + 190 = 0 0 + 11x + x2 = 0 + 190 11x + x2 = 0 + 190 Combine like terms: 0 + 190 = 190 11x + x2 = 190 The x term is 11x. Take half its coefficient (5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. 11x + 30.25 + x2 = 190 + 30.25 Reorder the terms: 30.25 + 11x + x2 = 190 + 30.25 Combine like terms: 190 + 30.25 = 220.25 30.25 + 11x + x2 = 220.25 Factor a perfect square on the left side: (x + 5.5)(x + 5.5) = 220.25 Calculate the square root of the right side: 14.84082208 Break this problem into two subproblems by setting (x + 5.5) equal to 14.84082208 and -14.84082208.Subproblem 1
x + 5.5 = 14.84082208 Simplifying x + 5.5 = 14.84082208 Reorder the terms: 5.5 + x = 14.84082208 Solving 5.5 + x = 14.84082208 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + x = 14.84082208 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = 14.84082208 + -5.5 x = 14.84082208 + -5.5 Combine like terms: 14.84082208 + -5.5 = 9.34082208 x = 9.34082208 Simplifying x = 9.34082208Subproblem 2
x + 5.5 = -14.84082208 Simplifying x + 5.5 = -14.84082208 Reorder the terms: 5.5 + x = -14.84082208 Solving 5.5 + x = -14.84082208 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + x = -14.84082208 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = -14.84082208 + -5.5 x = -14.84082208 + -5.5 Combine like terms: -14.84082208 + -5.5 = -20.34082208 x = -20.34082208 Simplifying x = -20.34082208Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.34082208, -20.34082208}
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