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Simplifying 5x2 + 11x + 3 = 9x2 + -1 Reorder the terms: 3 + 11x + 5x2 = 9x2 + -1 Reorder the terms: 3 + 11x + 5x2 = -1 + 9x2 Solving 3 + 11x + 5x2 = -1 + 9x2 Solving for variable 'x'. Reorder the terms: 3 + 1 + 11x + 5x2 + -9x2 = -1 + 9x2 + 1 + -9x2 Combine like terms: 3 + 1 = 4 4 + 11x + 5x2 + -9x2 = -1 + 9x2 + 1 + -9x2 Combine like terms: 5x2 + -9x2 = -4x2 4 + 11x + -4x2 = -1 + 9x2 + 1 + -9x2 Reorder the terms: 4 + 11x + -4x2 = -1 + 1 + 9x2 + -9x2 Combine like terms: -1 + 1 = 0 4 + 11x + -4x2 = 0 + 9x2 + -9x2 4 + 11x + -4x2 = 9x2 + -9x2 Combine like terms: 9x2 + -9x2 = 0 4 + 11x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -1 + -2.75x + x2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + -2.75x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + -2.75x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -2.75x + x2 = 0 + 1 -2.75x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 -2.75x + x2 = 1 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 = 1 + 1.890625 Reorder the terms: 1.890625 + -2.75x + x2 = 1 + 1.890625 Combine like terms: 1 + 1.890625 = 2.890625 1.890625 + -2.75x + x2 = 2.890625 Factor a perfect square on the left side: (x + -1.375)(x + -1.375) = 2.890625 Calculate the square root of the right side: 1.700183814 Break this problem into two subproblems by setting (x + -1.375) equal to 1.700183814 and -1.700183814.Subproblem 1
x + -1.375 = 1.700183814 Simplifying x + -1.375 = 1.700183814 Reorder the terms: -1.375 + x = 1.700183814 Solving -1.375 + x = 1.700183814 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 = 1.700183814 + 1.375 Combine like terms: -1.375 + 1.375 = 0.000 0.000 + x = 1.700183814 + 1.375 x = 1.700183814 + 1.375 Combine like terms: 1.700183814 + 1.375 = 3.075183814 x = 3.075183814 Simplifying x = 3.075183814Subproblem 2
x + -1.375 = -1.700183814 Simplifying x + -1.375 = -1.700183814 Reorder the terms: -1.375 + x = -1.700183814 Solving -1.375 + x = -1.700183814 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 = -1.700183814 + 1.375 Combine like terms: -1.375 + 1.375 = 0.000 0.000 + x = -1.700183814 + 1.375 x = -1.700183814 + 1.375 Combine like terms: -1.700183814 + 1.375 = -0.325183814 x = -0.325183814 Simplifying x = -0.325183814Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.075183814, -0.325183814}
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