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Simplifying x2 + -5.8x + 1 = 0 Reorder the terms: 1 + -5.8x + x2 = 0 Solving 1 + -5.8x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-1' to each side of the equation. 1 + -5.8x + -1 + x2 = 0 + -1 Reorder the terms: 1 + -1 + -5.8x + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -5.8x + x2 = 0 + -1 -5.8x + x2 = 0 + -1 Combine like terms: 0 + -1 = -1 -5.8x + x2 = -1 The x term is -5.8x. Take half its coefficient (-2.9). Square it (8.41) and add it to both sides. Add '8.41' to each side of the equation. -5.8x + 8.41 + x2 = -1 + 8.41 Reorder the terms: 8.41 + -5.8x + x2 = -1 + 8.41 Combine like terms: -1 + 8.41 = 7.41 8.41 + -5.8x + x2 = 7.41 Factor a perfect square on the left side: (x + -2.9)(x + -2.9) = 7.41 Calculate the square root of the right side: 2.722131518 Break this problem into two subproblems by setting (x + -2.9) equal to 2.722131518 and -2.722131518.Subproblem 1
x + -2.9 = 2.722131518 Simplifying x + -2.9 = 2.722131518 Reorder the terms: -2.9 + x = 2.722131518 Solving -2.9 + x = 2.722131518 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.9' to each side of the equation. -2.9 + 2.9 + x = 2.722131518 + 2.9 Combine like terms: -2.9 + 2.9 = 0.0 0.0 + x = 2.722131518 + 2.9 x = 2.722131518 + 2.9 Combine like terms: 2.722131518 + 2.9 = 5.622131518 x = 5.622131518 Simplifying x = 5.622131518Subproblem 2
x + -2.9 = -2.722131518 Simplifying x + -2.9 = -2.722131518 Reorder the terms: -2.9 + x = -2.722131518 Solving -2.9 + x = -2.722131518 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.9' to each side of the equation. -2.9 + 2.9 + x = -2.722131518 + 2.9 Combine like terms: -2.9 + 2.9 = 0.0 0.0 + x = -2.722131518 + 2.9 x = -2.722131518 + 2.9 Combine like terms: -2.722131518 + 2.9 = 0.177868482 x = 0.177868482 Simplifying x = 0.177868482Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.622131518, 0.177868482}
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