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Simplifying x2 + -4.36x + 3.15 = 0 Reorder the terms: 3.15 + -4.36x + x2 = 0 Solving 3.15 + -4.36x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-3.15' to each side of the equation. 3.15 + -4.36x + -3.15 + x2 = 0 + -3.15 Reorder the terms: 3.15 + -3.15 + -4.36x + x2 = 0 + -3.15 Combine like terms: 3.15 + -3.15 = 0.00 0.00 + -4.36x + x2 = 0 + -3.15 -4.36x + x2 = 0 + -3.15 Combine like terms: 0 + -3.15 = -3.15 -4.36x + x2 = -3.15 The x term is -4.36x. Take half its coefficient (-2.18). Square it (4.7524) and add it to both sides. Add '4.7524' to each side of the equation. -4.36x + 4.7524 + x2 = -3.15 + 4.7524 Reorder the terms: 4.7524 + -4.36x + x2 = -3.15 + 4.7524 Combine like terms: -3.15 + 4.7524 = 1.6024 4.7524 + -4.36x + x2 = 1.6024 Factor a perfect square on the left side: (x + -2.18)(x + -2.18) = 1.6024 Calculate the square root of the right side: 1.265859392 Break this problem into two subproblems by setting (x + -2.18) equal to 1.265859392 and -1.265859392.Subproblem 1
x + -2.18 = 1.265859392 Simplifying x + -2.18 = 1.265859392 Reorder the terms: -2.18 + x = 1.265859392 Solving -2.18 + x = 1.265859392 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.18' to each side of the equation. -2.18 + 2.18 + x = 1.265859392 + 2.18 Combine like terms: -2.18 + 2.18 = 0.00 0.00 + x = 1.265859392 + 2.18 x = 1.265859392 + 2.18 Combine like terms: 1.265859392 + 2.18 = 3.445859392 x = 3.445859392 Simplifying x = 3.445859392Subproblem 2
x + -2.18 = -1.265859392 Simplifying x + -2.18 = -1.265859392 Reorder the terms: -2.18 + x = -1.265859392 Solving -2.18 + x = -1.265859392 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.18' to each side of the equation. -2.18 + 2.18 + x = -1.265859392 + 2.18 Combine like terms: -2.18 + 2.18 = 0.00 0.00 + x = -1.265859392 + 2.18 x = -1.265859392 + 2.18 Combine like terms: -1.265859392 + 2.18 = 0.914140608 x = 0.914140608 Simplifying x = 0.914140608Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.445859392, 0.914140608}
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