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Simplifying 0 = -0.011x2 + x + 1.6 Reorder the terms: 0 = 1.6 + x + -0.011x2 Solving 0 = 1.6 + x + -0.011x2 Solving for variable 'x'. Combine like terms: 0 + -1.6 = -1.6 -1.6 + -1x + 0.011x2 = 1.6 + x + -0.011x2 + -1.6 + -1x + 0.011x2 Reorder the terms: -1.6 + -1x + 0.011x2 = 1.6 + -1.6 + x + -1x + -0.011x2 + 0.011x2 Combine like terms: 1.6 + -1.6 = 0.0 -1.6 + -1x + 0.011x2 = 0.0 + x + -1x + -0.011x2 + 0.011x2 -1.6 + -1x + 0.011x2 = x + -1x + -0.011x2 + 0.011x2 Combine like terms: x + -1x = 0 -1.6 + -1x + 0.011x2 = 0 + -0.011x2 + 0.011x2 -1.6 + -1x + 0.011x2 = -0.011x2 + 0.011x2 Combine like terms: -0.011x2 + 0.011x2 = 0.000 -1.6 + -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'. -145.4545455 + -90.90909091x + x2 = 0 Move the constant term to the right: Add '145.4545455' to each side of the equation. -145.4545455 + -90.90909091x + 145.4545455 + x2 = 0 + 145.4545455 Reorder the terms: -145.4545455 + 145.4545455 + -90.90909091x + x2 = 0 + 145.4545455 Combine like terms: -145.4545455 + 145.4545455 = 0.0000000 0.0000000 + -90.90909091x + x2 = 0 + 145.4545455 -90.90909091x + x2 = 0 + 145.4545455 Combine like terms: 0 + 145.4545455 = 145.4545455 -90.90909091x + x2 = 145.4545455 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 = 145.4545455 + 2066.115703 Reorder the terms: 2066.115703 + -90.90909091x + x2 = 145.4545455 + 2066.115703 Combine like terms: 145.4545455 + 2066.115703 = 2211.5702485 2066.115703 + -90.90909091x + x2 = 2211.5702485 Factor a perfect square on the left side: (x + -45.45454546)(x + -45.45454546) = 2211.5702485 Calculate the square root of the right side: 47.02733512 Break this problem into two subproblems by setting (x + -45.45454546) equal to 47.02733512 and -47.02733512.Subproblem 1
x + -45.45454546 = 47.02733512 Simplifying x + -45.45454546 = 47.02733512 Reorder the terms: -45.45454546 + x = 47.02733512 Solving -45.45454546 + x = 47.02733512 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 = 47.02733512 + 45.45454546 Combine like terms: -45.45454546 + 45.45454546 = 0.00000000 0.00000000 + x = 47.02733512 + 45.45454546 x = 47.02733512 + 45.45454546 Combine like terms: 47.02733512 + 45.45454546 = 92.48188058 x = 92.48188058 Simplifying x = 92.48188058Subproblem 2
x + -45.45454546 = -47.02733512 Simplifying x + -45.45454546 = -47.02733512 Reorder the terms: -45.45454546 + x = -47.02733512 Solving -45.45454546 + x = -47.02733512 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 = -47.02733512 + 45.45454546 Combine like terms: -45.45454546 + 45.45454546 = 0.00000000 0.00000000 + x = -47.02733512 + 45.45454546 x = -47.02733512 + 45.45454546 Combine like terms: -47.02733512 + 45.45454546 = -1.57278966 x = -1.57278966 Simplifying x = -1.57278966Solution
The solution to the problem is based on the solutions from the subproblems. x = {92.48188058, -1.57278966}
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