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Simplifying 2x2 + -2.00x + -0.39 = 0 Reorder the terms: -0.39 + -2.00x + 2x2 = 0 Solving -0.39 + -2.00x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -0.195 + -1x + x2 = 0 Move the constant term to the right: Add '0.195' to each side of the equation. -0.195 + -1x + 0.195 + x2 = 0 + 0.195 Reorder the terms: -0.195 + 0.195 + -1x + x2 = 0 + 0.195 Combine like terms: -0.195 + 0.195 = 0.000 0.000 + -1x + x2 = 0 + 0.195 -1x + x2 = 0 + 0.195 Combine like terms: 0 + 0.195 = 0.195 -1x + x2 = 0.195 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = 0.195 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 0.195 + 0.25 Combine like terms: 0.195 + 0.25 = 0.445 0.25 + -1x + x2 = 0.445 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 0.445 Calculate the square root of the right side: 0.667083203 Break this problem into two subproblems by setting (x + -0.5) equal to 0.667083203 and -0.667083203.Subproblem 1
x + -0.5 = 0.667083203 Simplifying x + -0.5 = 0.667083203 Reorder the terms: -0.5 + x = 0.667083203 Solving -0.5 + x = 0.667083203 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 0.667083203 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 0.667083203 + 0.5 x = 0.667083203 + 0.5 Combine like terms: 0.667083203 + 0.5 = 1.167083203 x = 1.167083203 Simplifying x = 1.167083203Subproblem 2
x + -0.5 = -0.667083203 Simplifying x + -0.5 = -0.667083203 Reorder the terms: -0.5 + x = -0.667083203 Solving -0.5 + x = -0.667083203 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -0.667083203 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -0.667083203 + 0.5 x = -0.667083203 + 0.5 Combine like terms: -0.667083203 + 0.5 = -0.167083203 x = -0.167083203 Simplifying x = -0.167083203Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.167083203, -0.167083203}
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