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Simplifying (3 + -2x)(3 + 2x) + 10x = 1 + -1x Multiply (3 + -2x) * (3 + 2x) (3(3 + 2x) + -2x * (3 + 2x)) + 10x = 1 + -1x ((3 * 3 + 2x * 3) + -2x * (3 + 2x)) + 10x = 1 + -1x ((9 + 6x) + -2x * (3 + 2x)) + 10x = 1 + -1x (9 + 6x + (3 * -2x + 2x * -2x)) + 10x = 1 + -1x (9 + 6x + (-6x + -4x2)) + 10x = 1 + -1x Combine like terms: 6x + -6x = 0 (9 + 0 + -4x2) + 10x = 1 + -1x (9 + -4x2) + 10x = 1 + -1x Reorder the terms: 9 + 10x + -4x2 = 1 + -1x Solving 9 + 10x + -4x2 = 1 + -1x Solving for variable 'x'. Reorder the terms: 9 + -1 + 10x + x + -4x2 = 1 + -1x + -1 + x Combine like terms: 9 + -1 = 8 8 + 10x + x + -4x2 = 1 + -1x + -1 + x Combine like terms: 10x + x = 11x 8 + 11x + -4x2 = 1 + -1x + -1 + x Reorder the terms: 8 + 11x + -4x2 = 1 + -1 + -1x + x Combine like terms: 1 + -1 = 0 8 + 11x + -4x2 = 0 + -1x + x 8 + 11x + -4x2 = -1x + x Combine like terms: -1x + x = 0 8 + 11x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -2 + -2.75x + x2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + -2.75x + 2 + x2 = 0 + 2 Reorder the terms: -2 + 2 + -2.75x + x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -2.75x + x2 = 0 + 2 -2.75x + x2 = 0 + 2 Combine like terms: 0 + 2 = 2 -2.75x + x2 = 2 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 + 1.890625 Reorder the terms: 1.890625 + -2.75x + x2 = 2 + 1.890625 Combine like terms: 2 + 1.890625 = 3.890625 1.890625 + -2.75x + x2 = 3.890625 Factor a perfect square on the left side: (x + -1.375)(x + -1.375) = 3.890625 Calculate the square root of the right side: 1.97246673 Break this problem into two subproblems by setting (x + -1.375) equal to 1.97246673 and -1.97246673.Subproblem 1
x + -1.375 = 1.97246673 Simplifying x + -1.375 = 1.97246673 Reorder the terms: -1.375 + x = 1.97246673 Solving -1.375 + x = 1.97246673 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 = 1.97246673 + 1.375 Combine like terms: -1.375 + 1.375 = 0.000 0.000 + x = 1.97246673 + 1.375 x = 1.97246673 + 1.375 Combine like terms: 1.97246673 + 1.375 = 3.34746673 x = 3.34746673 Simplifying x = 3.34746673Subproblem 2
x + -1.375 = -1.97246673 Simplifying x + -1.375 = -1.97246673 Reorder the terms: -1.375 + x = -1.97246673 Solving -1.375 + x = -1.97246673 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 = -1.97246673 + 1.375 Combine like terms: -1.375 + 1.375 = 0.000 0.000 + x = -1.97246673 + 1.375 x = -1.97246673 + 1.375 Combine like terms: -1.97246673 + 1.375 = -0.59746673 x = -0.59746673 Simplifying x = -0.59746673Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.34746673, -0.59746673}
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