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Simplifying x2 + -1.84x + 0.792 = 0 Reorder the terms: 0.792 + -1.84x + x2 = 0 Solving 0.792 + -1.84x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-0.792' to each side of the equation. 0.792 + -1.84x + -0.792 + x2 = 0 + -0.792 Reorder the terms: 0.792 + -0.792 + -1.84x + x2 = 0 + -0.792 Combine like terms: 0.792 + -0.792 = 0.000 0.000 + -1.84x + x2 = 0 + -0.792 -1.84x + x2 = 0 + -0.792 Combine like terms: 0 + -0.792 = -0.792 -1.84x + x2 = -0.792 The x term is -1.84x. Take half its coefficient (-0.92). Square it (0.8464) and add it to both sides. Add '0.8464' to each side of the equation. -1.84x + 0.8464 + x2 = -0.792 + 0.8464 Reorder the terms: 0.8464 + -1.84x + x2 = -0.792 + 0.8464 Combine like terms: -0.792 + 0.8464 = 0.0544 0.8464 + -1.84x + x2 = 0.0544 Factor a perfect square on the left side: (x + -0.92)(x + -0.92) = 0.0544 Calculate the square root of the right side: 0.233238076 Break this problem into two subproblems by setting (x + -0.92) equal to 0.233238076 and -0.233238076.Subproblem 1
x + -0.92 = 0.233238076 Simplifying x + -0.92 = 0.233238076 Reorder the terms: -0.92 + x = 0.233238076 Solving -0.92 + x = 0.233238076 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.92' to each side of the equation. -0.92 + 0.92 + x = 0.233238076 + 0.92 Combine like terms: -0.92 + 0.92 = 0.00 0.00 + x = 0.233238076 + 0.92 x = 0.233238076 + 0.92 Combine like terms: 0.233238076 + 0.92 = 1.153238076 x = 1.153238076 Simplifying x = 1.153238076Subproblem 2
x + -0.92 = -0.233238076 Simplifying x + -0.92 = -0.233238076 Reorder the terms: -0.92 + x = -0.233238076 Solving -0.92 + x = -0.233238076 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.92' to each side of the equation. -0.92 + 0.92 + x = -0.233238076 + 0.92 Combine like terms: -0.92 + 0.92 = 0.00 0.00 + x = -0.233238076 + 0.92 x = -0.233238076 + 0.92 Combine like terms: -0.233238076 + 0.92 = 0.686761924 x = 0.686761924 Simplifying x = 0.686761924Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.153238076, 0.686761924}
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