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Simplifying 2x2 + 2x + -19.41 = 0 Reorder the terms: -19.41 + 2x + 2x2 = 0 Solving -19.41 + 2x + 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'. -9.705 + x + x2 = 0 Move the constant term to the right: Add '9.705' to each side of the equation. -9.705 + x + 9.705 + x2 = 0 + 9.705 Reorder the terms: -9.705 + 9.705 + x + x2 = 0 + 9.705 Combine like terms: -9.705 + 9.705 = 0.000 0.000 + x + x2 = 0 + 9.705 x + x2 = 0 + 9.705 Combine like terms: 0 + 9.705 = 9.705 x + x2 = 9.705 The x term is x. 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. + 0.25 + x2 = 9.705 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 9.705 + 0.25 Combine like terms: 9.705 + 0.25 = 9.955 1.25 + x2 = 9.955 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 9.955 Calculate the square root of the right side: 3.155154513 Break this problem into two subproblems by setting (x + 0.5) equal to 3.155154513 and -3.155154513.Subproblem 1
x + 0.5 = 3.155154513 Simplifying x + 0.5 = 3.155154513 Reorder the terms: 0.5 + x = 3.155154513 Solving 0.5 + x = 3.155154513 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 = 3.155154513 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 3.155154513 + -0.5 x = 3.155154513 + -0.5 Combine like terms: 3.155154513 + -0.5 = 2.655154513 x = 2.655154513 Simplifying x = 2.655154513Subproblem 2
x + 0.5 = -3.155154513 Simplifying x + 0.5 = -3.155154513 Reorder the terms: 0.5 + x = -3.155154513 Solving 0.5 + x = -3.155154513 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 = -3.155154513 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -3.155154513 + -0.5 x = -3.155154513 + -0.5 Combine like terms: -3.155154513 + -0.5 = -3.655154513 x = -3.655154513 Simplifying x = -3.655154513Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.655154513, -3.655154513}
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