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Simplifying x2 + 0.82x + -0.2 = 0 Reorder the terms: -0.2 + 0.82x + x2 = 0 Solving -0.2 + 0.82x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '0.2' to each side of the equation. -0.2 + 0.82x + 0.2 + x2 = 0 + 0.2 Reorder the terms: -0.2 + 0.2 + 0.82x + x2 = 0 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + 0.82x + x2 = 0 + 0.2 0.82x + x2 = 0 + 0.2 Combine like terms: 0 + 0.2 = 0.2 0.82x + x2 = 0.2 The x term is 0.82x. Take half its coefficient (0.41). Square it (0.1681) and add it to both sides. Add '0.1681' to each side of the equation. 0.82x + 0.1681 + x2 = 0.2 + 0.1681 Reorder the terms: 0.1681 + 0.82x + x2 = 0.2 + 0.1681 Combine like terms: 0.2 + 0.1681 = 0.3681 0.1681 + 0.82x + x2 = 0.3681 Factor a perfect square on the left side: (x + 0.41)(x + 0.41) = 0.3681 Calculate the square root of the right side: 0.606712452 Break this problem into two subproblems by setting (x + 0.41) equal to 0.606712452 and -0.606712452.Subproblem 1
x + 0.41 = 0.606712452 Simplifying x + 0.41 = 0.606712452 Reorder the terms: 0.41 + x = 0.606712452 Solving 0.41 + x = 0.606712452 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.41' to each side of the equation. 0.41 + -0.41 + x = 0.606712452 + -0.41 Combine like terms: 0.41 + -0.41 = 0.00 0.00 + x = 0.606712452 + -0.41 x = 0.606712452 + -0.41 Combine like terms: 0.606712452 + -0.41 = 0.196712452 x = 0.196712452 Simplifying x = 0.196712452Subproblem 2
x + 0.41 = -0.606712452 Simplifying x + 0.41 = -0.606712452 Reorder the terms: 0.41 + x = -0.606712452 Solving 0.41 + x = -0.606712452 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.41' to each side of the equation. 0.41 + -0.41 + x = -0.606712452 + -0.41 Combine like terms: 0.41 + -0.41 = 0.00 0.00 + x = -0.606712452 + -0.41 x = -0.606712452 + -0.41 Combine like terms: -0.606712452 + -0.41 = -1.016712452 x = -1.016712452 Simplifying x = -1.016712452Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.196712452, -1.016712452}
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