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Simplifying 15 = -0.011x2 + x + 1.6 Reorder the terms: 15 = 1.6 + x + -0.011x2 Solving 15 = 1.6 + x + -0.011x2 Solving for variable 'x'. Combine like terms: 15 + -1.6 = 13.4 13.4 + -1x + 0.011x2 = 1.6 + x + -0.011x2 + -1.6 + -1x + 0.011x2 Reorder the terms: 13.4 + -1x + 0.011x2 = 1.6 + -1.6 + x + -1x + -0.011x2 + 0.011x2 Combine like terms: 1.6 + -1.6 = 0.0 13.4 + -1x + 0.011x2 = 0.0 + x + -1x + -0.011x2 + 0.011x2 13.4 + -1x + 0.011x2 = x + -1x + -0.011x2 + 0.011x2 Combine like terms: x + -1x = 0 13.4 + -1x + 0.011x2 = 0 + -0.011x2 + 0.011x2 13.4 + -1x + 0.011x2 = -0.011x2 + 0.011x2 Combine like terms: -0.011x2 + 0.011x2 = 0.000 13.4 + -1x + 0.011x2 = 0.000 Begin completing the square. Divide all terms by 0.011 the coefficient of the squared term: Divide each side by '0.011'. 1218.181818 + -90.90909091x + x2 = 0 Move the constant term to the right: Add '-1218.181818' to each side of the equation. 1218.181818 + -90.90909091x + -1218.181818 + x2 = 0 + -1218.181818 Reorder the terms: 1218.181818 + -1218.181818 + -90.90909091x + x2 = 0 + -1218.181818 Combine like terms: 1218.181818 + -1218.181818 = 0.000000 0.000000 + -90.90909091x + x2 = 0 + -1218.181818 -90.90909091x + x2 = 0 + -1218.181818 Combine like terms: 0 + -1218.181818 = -1218.181818 -90.90909091x + x2 = -1218.181818 The x term is -90.90909091x. Take half its coefficient (-45.45454546). Square it (2066.115703) and add it to both sides. Add '2066.115703' to each side of the equation. -90.90909091x + 2066.115703 + x2 = -1218.181818 + 2066.115703 Reorder the terms: 2066.115703 + -90.90909091x + x2 = -1218.181818 + 2066.115703 Combine like terms: -1218.181818 + 2066.115703 = 847.933885 2066.115703 + -90.90909091x + x2 = 847.933885 Factor a perfect square on the left side: (x + -45.45454546)(x + -45.45454546) = 847.933885 Calculate the square root of the right side: 29.119304336 Break this problem into two subproblems by setting (x + -45.45454546) equal to 29.119304336 and -29.119304336.Subproblem 1
x + -45.45454546 = 29.119304336 Simplifying x + -45.45454546 = 29.119304336 Reorder the terms: -45.45454546 + x = 29.119304336 Solving -45.45454546 + x = 29.119304336 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '45.45454546' to each side of the equation. -45.45454546 + 45.45454546 + x = 29.119304336 + 45.45454546 Combine like terms: -45.45454546 + 45.45454546 = 0.00000000 0.00000000 + x = 29.119304336 + 45.45454546 x = 29.119304336 + 45.45454546 Combine like terms: 29.119304336 + 45.45454546 = 74.573849796 x = 74.573849796 Simplifying x = 74.573849796Subproblem 2
x + -45.45454546 = -29.119304336 Simplifying x + -45.45454546 = -29.119304336 Reorder the terms: -45.45454546 + x = -29.119304336 Solving -45.45454546 + x = -29.119304336 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '45.45454546' to each side of the equation. -45.45454546 + 45.45454546 + x = -29.119304336 + 45.45454546 Combine like terms: -45.45454546 + 45.45454546 = 0.00000000 0.00000000 + x = -29.119304336 + 45.45454546 x = -29.119304336 + 45.45454546 Combine like terms: -29.119304336 + 45.45454546 = 16.335241124 x = 16.335241124 Simplifying x = 16.335241124Solution
The solution to the problem is based on the solutions from the subproblems. x = {74.573849796, 16.335241124}
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