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Simplifying 0.0825x2 + -0.924x + 1.824 = 0 Reorder the terms: 1.824 + -0.924x + 0.0825x2 = 0 Solving 1.824 + -0.924x + 0.0825x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.0825 the coefficient of the squared term: Divide each side by '0.0825'. 22.10909091 + -11.2x + x2 = 0 Move the constant term to the right: Add '-22.10909091' to each side of the equation. 22.10909091 + -11.2x + -22.10909091 + x2 = 0 + -22.10909091 Reorder the terms: 22.10909091 + -22.10909091 + -11.2x + x2 = 0 + -22.10909091 Combine like terms: 22.10909091 + -22.10909091 = 0.00000000 0.00000000 + -11.2x + x2 = 0 + -22.10909091 -11.2x + x2 = 0 + -22.10909091 Combine like terms: 0 + -22.10909091 = -22.10909091 -11.2x + x2 = -22.10909091 The x term is -11.2x. Take half its coefficient (-5.6). Square it (31.36) and add it to both sides. Add '31.36' to each side of the equation. -11.2x + 31.36 + x2 = -22.10909091 + 31.36 Reorder the terms: 31.36 + -11.2x + x2 = -22.10909091 + 31.36 Combine like terms: -22.10909091 + 31.36 = 9.25090909 31.36 + -11.2x + x2 = 9.25090909 Factor a perfect square on the left side: (x + -5.6)(x + -5.6) = 9.25090909 Calculate the square root of the right side: 3.041530715 Break this problem into two subproblems by setting (x + -5.6) equal to 3.041530715 and -3.041530715.Subproblem 1
x + -5.6 = 3.041530715 Simplifying x + -5.6 = 3.041530715 Reorder the terms: -5.6 + x = 3.041530715 Solving -5.6 + x = 3.041530715 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.6' to each side of the equation. -5.6 + 5.6 + x = 3.041530715 + 5.6 Combine like terms: -5.6 + 5.6 = 0.0 0.0 + x = 3.041530715 + 5.6 x = 3.041530715 + 5.6 Combine like terms: 3.041530715 + 5.6 = 8.641530715 x = 8.641530715 Simplifying x = 8.641530715Subproblem 2
x + -5.6 = -3.041530715 Simplifying x + -5.6 = -3.041530715 Reorder the terms: -5.6 + x = -3.041530715 Solving -5.6 + x = -3.041530715 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.6' to each side of the equation. -5.6 + 5.6 + x = -3.041530715 + 5.6 Combine like terms: -5.6 + 5.6 = 0.0 0.0 + x = -3.041530715 + 5.6 x = -3.041530715 + 5.6 Combine like terms: -3.041530715 + 5.6 = 2.558469285 x = 2.558469285 Simplifying x = 2.558469285Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.641530715, 2.558469285}
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