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Simplifying 100 = 10.032x + -0.01x2 + -9.843 Reorder the terms: 100 = -9.843 + 10.032x + -0.01x2 Solving 100 = -9.843 + 10.032x + -0.01x2 Solving for variable 'x'. Combine like terms: 100 + 9.843 = 109.843 109.843 + -10.032x + 0.01x2 = -9.843 + 10.032x + -0.01x2 + 9.843 + -10.032x + 0.01x2 Reorder the terms: 109.843 + -10.032x + 0.01x2 = -9.843 + 9.843 + 10.032x + -10.032x + -0.01x2 + 0.01x2 Combine like terms: -9.843 + 9.843 = 0.000 109.843 + -10.032x + 0.01x2 = 0.000 + 10.032x + -10.032x + -0.01x2 + 0.01x2 109.843 + -10.032x + 0.01x2 = 10.032x + -10.032x + -0.01x2 + 0.01x2 Combine like terms: 10.032x + -10.032x = 0.000 109.843 + -10.032x + 0.01x2 = 0.000 + -0.01x2 + 0.01x2 109.843 + -10.032x + 0.01x2 = -0.01x2 + 0.01x2 Combine like terms: -0.01x2 + 0.01x2 = 0.00 109.843 + -10.032x + 0.01x2 = 0.00 Begin completing the square. Divide all terms by 0.01 the coefficient of the squared term: Divide each side by '0.01'. 10984.3 + -1003.2x + x2 = 0 Move the constant term to the right: Add '-10984.3' to each side of the equation. 10984.3 + -1003.2x + -10984.3 + x2 = 0 + -10984.3 Reorder the terms: 10984.3 + -10984.3 + -1003.2x + x2 = 0 + -10984.3 Combine like terms: 10984.3 + -10984.3 = 0.0 0.0 + -1003.2x + x2 = 0 + -10984.3 -1003.2x + x2 = 0 + -10984.3 Combine like terms: 0 + -10984.3 = -10984.3 -1003.2x + x2 = -10984.3 The x term is -1003.2x. Take half its coefficient (-501.6). Square it (251602.56) and add it to both sides. Add '251602.56' to each side of the equation. -1003.2x + 251602.56 + x2 = -10984.3 + 251602.56 Reorder the terms: 251602.56 + -1003.2x + x2 = -10984.3 + 251602.56 Combine like terms: -10984.3 + 251602.56 = 240618.26 251602.56 + -1003.2x + x2 = 240618.26 Factor a perfect square on the left side: (x + -501.6)(x + -501.6) = 240618.26 Calculate the square root of the right side: 490.528551666 Break this problem into two subproblems by setting (x + -501.6) equal to 490.528551666 and -490.528551666.Subproblem 1
x + -501.6 = 490.528551666 Simplifying x + -501.6 = 490.528551666 Reorder the terms: -501.6 + x = 490.528551666 Solving -501.6 + x = 490.528551666 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '501.6' to each side of the equation. -501.6 + 501.6 + x = 490.528551666 + 501.6 Combine like terms: -501.6 + 501.6 = 0.0 0.0 + x = 490.528551666 + 501.6 x = 490.528551666 + 501.6 Combine like terms: 490.528551666 + 501.6 = 992.128551666 x = 992.128551666 Simplifying x = 992.128551666Subproblem 2
x + -501.6 = -490.528551666 Simplifying x + -501.6 = -490.528551666 Reorder the terms: -501.6 + x = -490.528551666 Solving -501.6 + x = -490.528551666 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '501.6' to each side of the equation. -501.6 + 501.6 + x = -490.528551666 + 501.6 Combine like terms: -501.6 + 501.6 = 0.0 0.0 + x = -490.528551666 + 501.6 x = -490.528551666 + 501.6 Combine like terms: -490.528551666 + 501.6 = 11.071448334 x = 11.071448334 Simplifying x = 11.071448334Solution
The solution to the problem is based on the solutions from the subproblems. x = {992.128551666, 11.071448334}
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