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Simplifying 4x2 + 11x + -13 = 0 Reorder the terms: -13 + 11x + 4x2 = 0 Solving -13 + 11x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -3.25 + 2.75x + x2 = 0 Move the constant term to the right: Add '3.25' to each side of the equation. -3.25 + 2.75x + 3.25 + x2 = 0 + 3.25 Reorder the terms: -3.25 + 3.25 + 2.75x + x2 = 0 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + 2.75x + x2 = 0 + 3.25 2.75x + x2 = 0 + 3.25 Combine like terms: 0 + 3.25 = 3.25 2.75x + x2 = 3.25 The x term is 2.75x. Take half its coefficient (1.375). Square it (1.890625) and add it to both sides. Add '1.890625' to each side of the equation. 2.75x + 1.890625 + x2 = 3.25 + 1.890625 Reorder the terms: 1.890625 + 2.75x + x2 = 3.25 + 1.890625 Combine like terms: 3.25 + 1.890625 = 5.140625 1.890625 + 2.75x + x2 = 5.140625 Factor a perfect square on the left side: (x + 1.375)(x + 1.375) = 5.140625 Calculate the square root of the right side: 2.267294643 Break this problem into two subproblems by setting (x + 1.375) equal to 2.267294643 and -2.267294643.Subproblem 1
x + 1.375 = 2.267294643 Simplifying x + 1.375 = 2.267294643 Reorder the terms: 1.375 + x = 2.267294643 Solving 1.375 + x = 2.267294643 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.375' to each side of the equation. 1.375 + -1.375 + x = 2.267294643 + -1.375 Combine like terms: 1.375 + -1.375 = 0.000 0.000 + x = 2.267294643 + -1.375 x = 2.267294643 + -1.375 Combine like terms: 2.267294643 + -1.375 = 0.892294643 x = 0.892294643 Simplifying x = 0.892294643Subproblem 2
x + 1.375 = -2.267294643 Simplifying x + 1.375 = -2.267294643 Reorder the terms: 1.375 + x = -2.267294643 Solving 1.375 + x = -2.267294643 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.375' to each side of the equation. 1.375 + -1.375 + x = -2.267294643 + -1.375 Combine like terms: 1.375 + -1.375 = 0.000 0.000 + x = -2.267294643 + -1.375 x = -2.267294643 + -1.375 Combine like terms: -2.267294643 + -1.375 = -3.642294643 x = -3.642294643 Simplifying x = -3.642294643Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.892294643, -3.642294643}
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