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Simplifying x2 + 4.62x + -0.462 = 0 Reorder the terms: -0.462 + 4.62x + x2 = 0 Solving -0.462 + 4.62x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '0.462' to each side of the equation. -0.462 + 4.62x + 0.462 + x2 = 0 + 0.462 Reorder the terms: -0.462 + 0.462 + 4.62x + x2 = 0 + 0.462 Combine like terms: -0.462 + 0.462 = 0.000 0.000 + 4.62x + x2 = 0 + 0.462 4.62x + x2 = 0 + 0.462 Combine like terms: 0 + 0.462 = 0.462 4.62x + x2 = 0.462 The x term is 4.62x. Take half its coefficient (2.31). Square it (5.3361) and add it to both sides. Add '5.3361' to each side of the equation. 4.62x + 5.3361 + x2 = 0.462 + 5.3361 Reorder the terms: 5.3361 + 4.62x + x2 = 0.462 + 5.3361 Combine like terms: 0.462 + 5.3361 = 5.7981 5.3361 + 4.62x + x2 = 5.7981 Factor a perfect square on the left side: (x + 2.31)(x + 2.31) = 5.7981 Calculate the square root of the right side: 2.407924417 Break this problem into two subproblems by setting (x + 2.31) equal to 2.407924417 and -2.407924417.Subproblem 1
x + 2.31 = 2.407924417 Simplifying x + 2.31 = 2.407924417 Reorder the terms: 2.31 + x = 2.407924417 Solving 2.31 + x = 2.407924417 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.31' to each side of the equation. 2.31 + -2.31 + x = 2.407924417 + -2.31 Combine like terms: 2.31 + -2.31 = 0.00 0.00 + x = 2.407924417 + -2.31 x = 2.407924417 + -2.31 Combine like terms: 2.407924417 + -2.31 = 0.097924417 x = 0.097924417 Simplifying x = 0.097924417Subproblem 2
x + 2.31 = -2.407924417 Simplifying x + 2.31 = -2.407924417 Reorder the terms: 2.31 + x = -2.407924417 Solving 2.31 + x = -2.407924417 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.31' to each side of the equation. 2.31 + -2.31 + x = -2.407924417 + -2.31 Combine like terms: 2.31 + -2.31 = 0.00 0.00 + x = -2.407924417 + -2.31 x = -2.407924417 + -2.31 Combine like terms: -2.407924417 + -2.31 = -4.717924417 x = -4.717924417 Simplifying x = -4.717924417Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.097924417, -4.717924417}
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