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Simplifying x2 + 0.76x + -0.62 = 0 Reorder the terms: -0.62 + 0.76x + x2 = 0 Solving -0.62 + 0.76x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '0.62' to each side of the equation. -0.62 + 0.76x + 0.62 + x2 = 0 + 0.62 Reorder the terms: -0.62 + 0.62 + 0.76x + x2 = 0 + 0.62 Combine like terms: -0.62 + 0.62 = 0.00 0.00 + 0.76x + x2 = 0 + 0.62 0.76x + x2 = 0 + 0.62 Combine like terms: 0 + 0.62 = 0.62 0.76x + x2 = 0.62 The x term is 0.76x. Take half its coefficient (0.38). Square it (0.1444) and add it to both sides. Add '0.1444' to each side of the equation. 0.76x + 0.1444 + x2 = 0.62 + 0.1444 Reorder the terms: 0.1444 + 0.76x + x2 = 0.62 + 0.1444 Combine like terms: 0.62 + 0.1444 = 0.7644 0.1444 + 0.76x + x2 = 0.7644 Factor a perfect square on the left side: (x + 0.38)(x + 0.38) = 0.7644 Calculate the square root of the right side: 0.87429972 Break this problem into two subproblems by setting (x + 0.38) equal to 0.87429972 and -0.87429972.Subproblem 1
x + 0.38 = 0.87429972 Simplifying x + 0.38 = 0.87429972 Reorder the terms: 0.38 + x = 0.87429972 Solving 0.38 + x = 0.87429972 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.38' to each side of the equation. 0.38 + -0.38 + x = 0.87429972 + -0.38 Combine like terms: 0.38 + -0.38 = 0.00 0.00 + x = 0.87429972 + -0.38 x = 0.87429972 + -0.38 Combine like terms: 0.87429972 + -0.38 = 0.49429972 x = 0.49429972 Simplifying x = 0.49429972Subproblem 2
x + 0.38 = -0.87429972 Simplifying x + 0.38 = -0.87429972 Reorder the terms: 0.38 + x = -0.87429972 Solving 0.38 + x = -0.87429972 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.38' to each side of the equation. 0.38 + -0.38 + x = -0.87429972 + -0.38 Combine like terms: 0.38 + -0.38 = 0.00 0.00 + x = -0.87429972 + -0.38 x = -0.87429972 + -0.38 Combine like terms: -0.87429972 + -0.38 = -1.25429972 x = -1.25429972 Simplifying x = -1.25429972Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.49429972, -1.25429972}
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