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Simplifying x2 + -52.977x + 55 = 0 Reorder the terms: 55 + -52.977x + x2 = 0 Solving 55 + -52.977x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-55' to each side of the equation. 55 + -52.977x + -55 + x2 = 0 + -55 Reorder the terms: 55 + -55 + -52.977x + x2 = 0 + -55 Combine like terms: 55 + -55 = 0 0 + -52.977x + x2 = 0 + -55 -52.977x + x2 = 0 + -55 Combine like terms: 0 + -55 = -55 -52.977x + x2 = -55 The x term is -52.977x. Take half its coefficient (-26.4885). Square it (701.6406323) and add it to both sides. Add '701.6406323' to each side of the equation. -52.977x + 701.6406323 + x2 = -55 + 701.6406323 Reorder the terms: 701.6406323 + -52.977x + x2 = -55 + 701.6406323 Combine like terms: -55 + 701.6406323 = 646.6406323 701.6406323 + -52.977x + x2 = 646.6406323 Factor a perfect square on the left side: (x + -26.4885)(x + -26.4885) = 646.6406323 Calculate the square root of the right side: 25.429129602 Break this problem into two subproblems by setting (x + -26.4885) equal to 25.429129602 and -25.429129602.Subproblem 1
x + -26.4885 = 25.429129602 Simplifying x + -26.4885 = 25.429129602 Reorder the terms: -26.4885 + x = 25.429129602 Solving -26.4885 + x = 25.429129602 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '26.4885' to each side of the equation. -26.4885 + 26.4885 + x = 25.429129602 + 26.4885 Combine like terms: -26.4885 + 26.4885 = 0.0000 0.0000 + x = 25.429129602 + 26.4885 x = 25.429129602 + 26.4885 Combine like terms: 25.429129602 + 26.4885 = 51.917629602 x = 51.917629602 Simplifying x = 51.917629602Subproblem 2
x + -26.4885 = -25.429129602 Simplifying x + -26.4885 = -25.429129602 Reorder the terms: -26.4885 + x = -25.429129602 Solving -26.4885 + x = -25.429129602 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '26.4885' to each side of the equation. -26.4885 + 26.4885 + x = -25.429129602 + 26.4885 Combine like terms: -26.4885 + 26.4885 = 0.0000 0.0000 + x = -25.429129602 + 26.4885 x = -25.429129602 + 26.4885 Combine like terms: -25.429129602 + 26.4885 = 1.059370398 x = 1.059370398 Simplifying x = 1.059370398Solution
The solution to the problem is based on the solutions from the subproblems. x = {51.917629602, 1.059370398}
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