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Simplifying 22 = 0.013x2 + -1.19x + 28.24 Reorder the terms: 22 = 28.24 + -1.19x + 0.013x2 Solving 22 = 28.24 + -1.19x + 0.013x2 Solving for variable 'x'. Combine like terms: 22 + -28.24 = -6.24 -6.24 + 1.19x + -0.013x2 = 28.24 + -1.19x + 0.013x2 + -28.24 + 1.19x + -0.013x2 Reorder the terms: -6.24 + 1.19x + -0.013x2 = 28.24 + -28.24 + -1.19x + 1.19x + 0.013x2 + -0.013x2 Combine like terms: 28.24 + -28.24 = 0.00 -6.24 + 1.19x + -0.013x2 = 0.00 + -1.19x + 1.19x + 0.013x2 + -0.013x2 -6.24 + 1.19x + -0.013x2 = -1.19x + 1.19x + 0.013x2 + -0.013x2 Combine like terms: -1.19x + 1.19x = 0.00 -6.24 + 1.19x + -0.013x2 = 0.00 + 0.013x2 + -0.013x2 -6.24 + 1.19x + -0.013x2 = 0.013x2 + -0.013x2 Combine like terms: 0.013x2 + -0.013x2 = 0.000 -6.24 + 1.19x + -0.013x2 = 0.000 Begin completing the square. Divide all terms by -0.013 the coefficient of the squared term: Divide each side by '-0.013'. 480 + -91.53846154x + x2 = 0 Move the constant term to the right: Add '-480' to each side of the equation. 480 + -91.53846154x + -480 + x2 = 0 + -480 Reorder the terms: 480 + -480 + -91.53846154x + x2 = 0 + -480 Combine like terms: 480 + -480 = 0 0 + -91.53846154x + x2 = 0 + -480 -91.53846154x + x2 = 0 + -480 Combine like terms: 0 + -480 = -480 -91.53846154x + x2 = -480 The x term is -91.53846154x. Take half its coefficient (-45.76923077). Square it (2094.822485) and add it to both sides. Add '2094.822485' to each side of the equation. -91.53846154x + 2094.822485 + x2 = -480 + 2094.822485 Reorder the terms: 2094.822485 + -91.53846154x + x2 = -480 + 2094.822485 Combine like terms: -480 + 2094.822485 = 1614.822485 2094.822485 + -91.53846154x + x2 = 1614.822485 Factor a perfect square on the left side: (x + -45.76923077)(x + -45.76923077) = 1614.822485 Calculate the square root of the right side: 40.184853925 Break this problem into two subproblems by setting (x + -45.76923077) equal to 40.184853925 and -40.184853925.Subproblem 1
x + -45.76923077 = 40.184853925 Simplifying x + -45.76923077 = 40.184853925 Reorder the terms: -45.76923077 + x = 40.184853925 Solving -45.76923077 + x = 40.184853925 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '45.76923077' to each side of the equation. -45.76923077 + 45.76923077 + x = 40.184853925 + 45.76923077 Combine like terms: -45.76923077 + 45.76923077 = 0.00000000 0.00000000 + x = 40.184853925 + 45.76923077 x = 40.184853925 + 45.76923077 Combine like terms: 40.184853925 + 45.76923077 = 85.954084695 x = 85.954084695 Simplifying x = 85.954084695Subproblem 2
x + -45.76923077 = -40.184853925 Simplifying x + -45.76923077 = -40.184853925 Reorder the terms: -45.76923077 + x = -40.184853925 Solving -45.76923077 + x = -40.184853925 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '45.76923077' to each side of the equation. -45.76923077 + 45.76923077 + x = -40.184853925 + 45.76923077 Combine like terms: -45.76923077 + 45.76923077 = 0.00000000 0.00000000 + x = -40.184853925 + 45.76923077 x = -40.184853925 + 45.76923077 Combine like terms: -40.184853925 + 45.76923077 = 5.584376845 x = 5.584376845 Simplifying x = 5.584376845Solution
The solution to the problem is based on the solutions from the subproblems. x = {85.954084695, 5.584376845}
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