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Simplifying (x + 4)(17x + -4) = 2 Reorder the terms: (4 + x)(17x + -4) = 2 Reorder the terms: (4 + x)(-4 + 17x) = 2 Multiply (4 + x) * (-4 + 17x) (4(-4 + 17x) + x(-4 + 17x)) = 2 ((-4 * 4 + 17x * 4) + x(-4 + 17x)) = 2 ((-16 + 68x) + x(-4 + 17x)) = 2 (-16 + 68x + (-4 * x + 17x * x)) = 2 (-16 + 68x + (-4x + 17x2)) = 2 Combine like terms: 68x + -4x = 64x (-16 + 64x + 17x2) = 2 Solving -16 + 64x + 17x2 = 2 Solving for variable 'x'. Reorder the terms: -16 + -2 + 64x + 17x2 = 2 + -2 Combine like terms: -16 + -2 = -18 -18 + 64x + 17x2 = 2 + -2 Combine like terms: 2 + -2 = 0 -18 + 64x + 17x2 = 0 Begin completing the square. Divide all terms by 17 the coefficient of the squared term: Divide each side by '17'. -1.058823529 + 3.764705882x + x2 = 0 Move the constant term to the right: Add '1.058823529' to each side of the equation. -1.058823529 + 3.764705882x + 1.058823529 + x2 = 0 + 1.058823529 Reorder the terms: -1.058823529 + 1.058823529 + 3.764705882x + x2 = 0 + 1.058823529 Combine like terms: -1.058823529 + 1.058823529 = 0.000000000 0.000000000 + 3.764705882x + x2 = 0 + 1.058823529 3.764705882x + x2 = 0 + 1.058823529 Combine like terms: 0 + 1.058823529 = 1.058823529 3.764705882x + x2 = 1.058823529 The x term is 3.764705882x. Take half its coefficient (1.882352941). Square it (3.543252594) and add it to both sides. Add '3.543252594' to each side of the equation. 3.764705882x + 3.543252594 + x2 = 1.058823529 + 3.543252594 Reorder the terms: 3.543252594 + 3.764705882x + x2 = 1.058823529 + 3.543252594 Combine like terms: 1.058823529 + 3.543252594 = 4.602076123 3.543252594 + 3.764705882x + x2 = 4.602076123 Factor a perfect square on the left side: (x + 1.882352941)(x + 1.882352941) = 4.602076123 Calculate the square root of the right side: 2.145245003 Break this problem into two subproblems by setting (x + 1.882352941) equal to 2.145245003 and -2.145245003.Subproblem 1
x + 1.882352941 = 2.145245003 Simplifying x + 1.882352941 = 2.145245003 Reorder the terms: 1.882352941 + x = 2.145245003 Solving 1.882352941 + x = 2.145245003 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.882352941' to each side of the equation. 1.882352941 + -1.882352941 + x = 2.145245003 + -1.882352941 Combine like terms: 1.882352941 + -1.882352941 = 0.000000000 0.000000000 + x = 2.145245003 + -1.882352941 x = 2.145245003 + -1.882352941 Combine like terms: 2.145245003 + -1.882352941 = 0.262892062 x = 0.262892062 Simplifying x = 0.262892062Subproblem 2
x + 1.882352941 = -2.145245003 Simplifying x + 1.882352941 = -2.145245003 Reorder the terms: 1.882352941 + x = -2.145245003 Solving 1.882352941 + x = -2.145245003 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.882352941' to each side of the equation. 1.882352941 + -1.882352941 + x = -2.145245003 + -1.882352941 Combine like terms: 1.882352941 + -1.882352941 = 0.000000000 0.000000000 + x = -2.145245003 + -1.882352941 x = -2.145245003 + -1.882352941 Combine like terms: -2.145245003 + -1.882352941 = -4.027597944 x = -4.027597944 Simplifying x = -4.027597944Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.262892062, -4.027597944}
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