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Simplifying [(11x)(10x + 11)] + -1[(16x + 14) + -1(10x + 16)] = 0 Remove parenthesis around (11x) [11x(10x + 11)] + -1[(16x + 14) + -1(10x + 16)] = 0 Reorder the terms: [11x(11 + 10x)] + -1[(16x + 14) + -1(10x + 16)] = 0 [(11 * 11x + 10x * 11x)] + -1[(16x + 14) + -1(10x + 16)] = 0 [(121x + 110x2)] + -1[(16x + 14) + -1(10x + 16)] = 0 [121x + 110x2] + -1[(16x + 14) + -1(10x + 16)] = 0 Remove brackets around [121x + 110x2] 121x + 110x2 + -1[(16x + 14) + -1(10x + 16)] = 0 Reorder the terms: 121x + 110x2 + -1[(14 + 16x) + -1(10x + 16)] = 0 Remove parenthesis around (14 + 16x) 121x + 110x2 + -1[14 + 16x + -1(10x + 16)] = 0 Reorder the terms: 121x + 110x2 + -1[14 + 16x + -1(16 + 10x)] = 0 121x + 110x2 + -1[14 + 16x + (16 * -1 + 10x * -1)] = 0 121x + 110x2 + -1[14 + 16x + (-16 + -10x)] = 0 Reorder the terms: 121x + 110x2 + -1[14 + -16 + 16x + -10x] = 0 Combine like terms: 14 + -16 = -2 121x + 110x2 + -1[-2 + 16x + -10x] = 0 Combine like terms: 16x + -10x = 6x 121x + 110x2 + -1[-2 + 6x] = 0 121x + 110x2 + [-2 * -1 + 6x * -1] = 0 121x + 110x2 + [2 + -6x] = 0 Reorder the terms: 2 + 121x + -6x + 110x2 = 0 Combine like terms: 121x + -6x = 115x 2 + 115x + 110x2 = 0 Solving 2 + 115x + 110x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 110 the coefficient of the squared term: Divide each side by '110'. 0.01818181818 + 1.045454545x + x2 = 0.0 Move the constant term to the right: Add '-0.01818181818' to each side of the equation. 0.01818181818 + 1.045454545x + -0.01818181818 + x2 = 0.0 + -0.01818181818 Reorder the terms: 0.01818181818 + -0.01818181818 + 1.045454545x + x2 = 0.0 + -0.01818181818 Combine like terms: 0.01818181818 + -0.01818181818 = 0.00000000000 0.00000000000 + 1.045454545x + x2 = 0.0 + -0.01818181818 1.045454545x + x2 = 0.0 + -0.01818181818 Combine like terms: 0.0 + -0.01818181818 = -0.01818181818 1.045454545x + x2 = -0.01818181818 The x term is 1.045454545x. Take half its coefficient (0.5227272725). Square it (0.2732438014) and add it to both sides. Add '0.2732438014' to each side of the equation. 1.045454545x + 0.2732438014 + x2 = -0.01818181818 + 0.2732438014 Reorder the terms: 0.2732438014 + 1.045454545x + x2 = -0.01818181818 + 0.2732438014 Combine like terms: -0.01818181818 + 0.2732438014 = 0.25506198322 0.2732438014 + 1.045454545x + x2 = 0.25506198322 Factor a perfect square on the left side: (x + 0.5227272725)(x + 0.5227272725) = 0.25506198322 Calculate the square root of the right side: 0.505036616 Break this problem into two subproblems by setting (x + 0.5227272725) equal to 0.505036616 and -0.505036616.Subproblem 1
x + 0.5227272725 = 0.505036616 Simplifying x + 0.5227272725 = 0.505036616 Reorder the terms: 0.5227272725 + x = 0.505036616 Solving 0.5227272725 + x = 0.505036616 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5227272725' to each side of the equation. 0.5227272725 + -0.5227272725 + x = 0.505036616 + -0.5227272725 Combine like terms: 0.5227272725 + -0.5227272725 = 0.0000000000 0.0000000000 + x = 0.505036616 + -0.5227272725 x = 0.505036616 + -0.5227272725 Combine like terms: 0.505036616 + -0.5227272725 = -0.0176906565 x = -0.0176906565 Simplifying x = -0.0176906565Subproblem 2
x + 0.5227272725 = -0.505036616 Simplifying x + 0.5227272725 = -0.505036616 Reorder the terms: 0.5227272725 + x = -0.505036616 Solving 0.5227272725 + x = -0.505036616 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5227272725' to each side of the equation. 0.5227272725 + -0.5227272725 + x = -0.505036616 + -0.5227272725 Combine like terms: 0.5227272725 + -0.5227272725 = 0.0000000000 0.0000000000 + x = -0.505036616 + -0.5227272725 x = -0.505036616 + -0.5227272725 Combine like terms: -0.505036616 + -0.5227272725 = -1.0277638885 x = -1.0277638885 Simplifying x = -1.0277638885Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.0176906565, -1.0277638885}
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