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Simplifying 4x2 + 11x = 9 Reorder the terms: 11x + 4x2 = 9 Solving 11x + 4x2 = 9 Solving for variable 'x'. Reorder the terms: -9 + 11x + 4x2 = 9 + -9 Combine like terms: 9 + -9 = 0 -9 + 11x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -2.25 + 2.75x + x2 = 0 Move the constant term to the right: Add '2.25' to each side of the equation. -2.25 + 2.75x + 2.25 + x2 = 0 + 2.25 Reorder the terms: -2.25 + 2.25 + 2.75x + x2 = 0 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + 2.75x + x2 = 0 + 2.25 2.75x + x2 = 0 + 2.25 Combine like terms: 0 + 2.25 = 2.25 2.75x + x2 = 2.25 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 = 2.25 + 1.890625 Reorder the terms: 1.890625 + 2.75x + x2 = 2.25 + 1.890625 Combine like terms: 2.25 + 1.890625 = 4.140625 1.890625 + 2.75x + x2 = 4.140625 Factor a perfect square on the left side: (x + 1.375)(x + 1.375) = 4.140625 Calculate the square root of the right side: 2.034852575 Break this problem into two subproblems by setting (x + 1.375) equal to 2.034852575 and -2.034852575.Subproblem 1
x + 1.375 = 2.034852575 Simplifying x + 1.375 = 2.034852575 Reorder the terms: 1.375 + x = 2.034852575 Solving 1.375 + x = 2.034852575 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 = 2.034852575 + -1.375 Combine like terms: 1.375 + -1.375 = 0.000 0.000 + x = 2.034852575 + -1.375 x = 2.034852575 + -1.375 Combine like terms: 2.034852575 + -1.375 = 0.659852575 x = 0.659852575 Simplifying x = 0.659852575Subproblem 2
x + 1.375 = -2.034852575 Simplifying x + 1.375 = -2.034852575 Reorder the terms: 1.375 + x = -2.034852575 Solving 1.375 + x = -2.034852575 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 = -2.034852575 + -1.375 Combine like terms: 1.375 + -1.375 = 0.000 0.000 + x = -2.034852575 + -1.375 x = -2.034852575 + -1.375 Combine like terms: -2.034852575 + -1.375 = -3.409852575 x = -3.409852575 Simplifying x = -3.409852575Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.659852575, -3.409852575}
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