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Simplifying x2 + -7x + -16.5 = 24.5 Reorder the terms: -16.5 + -7x + x2 = 24.5 Solving -16.5 + -7x + x2 = 24.5 Solving for variable 'x'. Reorder the terms: -16.5 + -24.5 + -7x + x2 = 24.5 + -24.5 Combine like terms: -16.5 + -24.5 = -41 -41 + -7x + x2 = 24.5 + -24.5 Combine like terms: 24.5 + -24.5 = 0.0 -41 + -7x + x2 = 0.0 Begin completing the square. Move the constant term to the right: Add '41' to each side of the equation. -41 + -7x + 41 + x2 = 0.0 + 41 Reorder the terms: -41 + 41 + -7x + x2 = 0.0 + 41 Combine like terms: -41 + 41 = 0 0 + -7x + x2 = 0.0 + 41 -7x + x2 = 0.0 + 41 Combine like terms: 0.0 + 41 = 41 -7x + x2 = 41 The x term is -7x. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7x + 12.25 + x2 = 41 + 12.25 Reorder the terms: 12.25 + -7x + x2 = 41 + 12.25 Combine like terms: 41 + 12.25 = 53.25 12.25 + -7x + x2 = 53.25 Factor a perfect square on the left side: (x + -3.5)(x + -3.5) = 53.25 Calculate the square root of the right side: 7.29725976 Break this problem into two subproblems by setting (x + -3.5) equal to 7.29725976 and -7.29725976.Subproblem 1
x + -3.5 = 7.29725976 Simplifying x + -3.5 = 7.29725976 Reorder the terms: -3.5 + x = 7.29725976 Solving -3.5 + x = 7.29725976 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = 7.29725976 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = 7.29725976 + 3.5 x = 7.29725976 + 3.5 Combine like terms: 7.29725976 + 3.5 = 10.79725976 x = 10.79725976 Simplifying x = 10.79725976Subproblem 2
x + -3.5 = -7.29725976 Simplifying x + -3.5 = -7.29725976 Reorder the terms: -3.5 + x = -7.29725976 Solving -3.5 + x = -7.29725976 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = -7.29725976 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = -7.29725976 + 3.5 x = -7.29725976 + 3.5 Combine like terms: -7.29725976 + 3.5 = -3.79725976 x = -3.79725976 Simplifying x = -3.79725976Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.79725976, -3.79725976}
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