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Simplifying 0 = 9 + -1(17.54x) + -1(1.54) * x2 Remove parenthesis around (17.54x) 0 = 9 + -1 * 17.54x + -1(1.54) * x2 Multiply -1 * 17.54 0 = 9 + -17.54x + -1(1.54) * x2 Multiply -1 * 1.54 0 = 9 + -17.54x + -1.54x2 Solving 0 = 9 + -17.54x + -1.54x2 Solving for variable 'x'. Combine like terms: 0 + -9 = -9 -9 + 17.54x + 1.54x2 = 9 + -17.54x + -1.54x2 + -9 + 17.54x + 1.54x2 Reorder the terms: -9 + 17.54x + 1.54x2 = 9 + -9 + -17.54x + 17.54x + -1.54x2 + 1.54x2 Combine like terms: 9 + -9 = 0 -9 + 17.54x + 1.54x2 = 0 + -17.54x + 17.54x + -1.54x2 + 1.54x2 -9 + 17.54x + 1.54x2 = -17.54x + 17.54x + -1.54x2 + 1.54x2 Combine like terms: -17.54x + 17.54x = 0.00 -9 + 17.54x + 1.54x2 = 0.00 + -1.54x2 + 1.54x2 -9 + 17.54x + 1.54x2 = -1.54x2 + 1.54x2 Combine like terms: -1.54x2 + 1.54x2 = 0.00 -9 + 17.54x + 1.54x2 = 0.00 Begin completing the square. Divide all terms by 1.54 the coefficient of the squared term: Divide each side by '1.54'. -5.844155844 + 11.38961039x + x2 = 0 Move the constant term to the right: Add '5.844155844' to each side of the equation. -5.844155844 + 11.38961039x + 5.844155844 + x2 = 0 + 5.844155844 Reorder the terms: -5.844155844 + 5.844155844 + 11.38961039x + x2 = 0 + 5.844155844 Combine like terms: -5.844155844 + 5.844155844 = 0.000000000 0.000000000 + 11.38961039x + x2 = 0 + 5.844155844 11.38961039x + x2 = 0 + 5.844155844 Combine like terms: 0 + 5.844155844 = 5.844155844 11.38961039x + x2 = 5.844155844 The x term is 11.38961039x. Take half its coefficient (5.694805195). Square it (32.43080621) and add it to both sides. Add '32.43080621' to each side of the equation. 11.38961039x + 32.43080621 + x2 = 5.844155844 + 32.43080621 Reorder the terms: 32.43080621 + 11.38961039x + x2 = 5.844155844 + 32.43080621 Combine like terms: 5.844155844 + 32.43080621 = 38.274962054 32.43080621 + 11.38961039x + x2 = 38.274962054 Factor a perfect square on the left side: (x + 5.694805195)(x + 5.694805195) = 38.274962054 Calculate the square root of the right side: 6.186676172 Break this problem into two subproblems by setting (x + 5.694805195) equal to 6.186676172 and -6.186676172.Subproblem 1
x + 5.694805195 = 6.186676172 Simplifying x + 5.694805195 = 6.186676172 Reorder the terms: 5.694805195 + x = 6.186676172 Solving 5.694805195 + x = 6.186676172 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.694805195' to each side of the equation. 5.694805195 + -5.694805195 + x = 6.186676172 + -5.694805195 Combine like terms: 5.694805195 + -5.694805195 = 0.000000000 0.000000000 + x = 6.186676172 + -5.694805195 x = 6.186676172 + -5.694805195 Combine like terms: 6.186676172 + -5.694805195 = 0.491870977 x = 0.491870977 Simplifying x = 0.491870977Subproblem 2
x + 5.694805195 = -6.186676172 Simplifying x + 5.694805195 = -6.186676172 Reorder the terms: 5.694805195 + x = -6.186676172 Solving 5.694805195 + x = -6.186676172 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.694805195' to each side of the equation. 5.694805195 + -5.694805195 + x = -6.186676172 + -5.694805195 Combine like terms: 5.694805195 + -5.694805195 = 0.000000000 0.000000000 + x = -6.186676172 + -5.694805195 x = -6.186676172 + -5.694805195 Combine like terms: -6.186676172 + -5.694805195 = -11.881481367 x = -11.881481367 Simplifying x = -11.881481367Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.491870977, -11.881481367}
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