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Simplifying 5x2 + 11x + -1 = 0 Reorder the terms: -1 + 11x + 5x2 = 0 Solving -1 + 11x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -0.2 + 2.2x + x2 = 0 Move the constant term to the right: Add '0.2' to each side of the equation. -0.2 + 2.2x + 0.2 + x2 = 0 + 0.2 Reorder the terms: -0.2 + 0.2 + 2.2x + x2 = 0 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + 2.2x + x2 = 0 + 0.2 2.2x + x2 = 0 + 0.2 Combine like terms: 0 + 0.2 = 0.2 2.2x + x2 = 0.2 The x term is 2.2x. Take half its coefficient (1.1). Square it (1.21) and add it to both sides. Add '1.21' to each side of the equation. 2.2x + 1.21 + x2 = 0.2 + 1.21 Reorder the terms: 1.21 + 2.2x + x2 = 0.2 + 1.21 Combine like terms: 0.2 + 1.21 = 1.41 1.21 + 2.2x + x2 = 1.41 Factor a perfect square on the left side: (x + 1.1)(x + 1.1) = 1.41 Calculate the square root of the right side: 1.187434209 Break this problem into two subproblems by setting (x + 1.1) equal to 1.187434209 and -1.187434209.Subproblem 1
x + 1.1 = 1.187434209 Simplifying x + 1.1 = 1.187434209 Reorder the terms: 1.1 + x = 1.187434209 Solving 1.1 + x = 1.187434209 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.1' to each side of the equation. 1.1 + -1.1 + x = 1.187434209 + -1.1 Combine like terms: 1.1 + -1.1 = 0.0 0.0 + x = 1.187434209 + -1.1 x = 1.187434209 + -1.1 Combine like terms: 1.187434209 + -1.1 = 0.087434209 x = 0.087434209 Simplifying x = 0.087434209Subproblem 2
x + 1.1 = -1.187434209 Simplifying x + 1.1 = -1.187434209 Reorder the terms: 1.1 + x = -1.187434209 Solving 1.1 + x = -1.187434209 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.1' to each side of the equation. 1.1 + -1.1 + x = -1.187434209 + -1.1 Combine like terms: 1.1 + -1.1 = 0.0 0.0 + x = -1.187434209 + -1.1 x = -1.187434209 + -1.1 Combine like terms: -1.187434209 + -1.1 = -2.287434209 x = -2.287434209 Simplifying x = -2.287434209Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.087434209, -2.287434209}
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