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Simplifying (0.013x2) + -1.19x + 28.24 = 9 Reorder the terms: 28.24 + -1.19x + (0.013x2) = 9 Solving 28.24 + -1.19x + (0.013x2) = 9 Solving for variable 'x'. Reorder the terms: 28.24 + -9 + -1.19x + (0.013x2) = 9 + -9 Combine like terms: 28.24 + -9 = 19.24 19.24 + -1.19x + (0.013x2) = 9 + -9 Combine like terms: 9 + -9 = 0 19.24 + -1.19x + (0.013x2) = 0 Begin completing the square. Divide all terms by 0.013 the coefficient of the squared term: Divide each side by '0.013'. 1480 + -91.53846154x + x2 = 0 Move the constant term to the right: Add '-1480' to each side of the equation. 1480 + -91.53846154x + -1480 + x2 = 0 + -1480 Reorder the terms: 1480 + -1480 + -91.53846154x + x2 = 0 + -1480 Combine like terms: 1480 + -1480 = 0 0 + -91.53846154x + x2 = 0 + -1480 -91.53846154x + x2 = 0 + -1480 Combine like terms: 0 + -1480 = -1480 -91.53846154x + x2 = -1480 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 = -1480 + 2094.822485 Reorder the terms: 2094.822485 + -91.53846154x + x2 = -1480 + 2094.822485 Combine like terms: -1480 + 2094.822485 = 614.822485 2094.822485 + -91.53846154x + x2 = 614.822485 Factor a perfect square on the left side: ((x) + -45.76923077)((x) + -45.76923077) = 614.822485 Calculate the square root of the right side: 24.795614229 Break this problem into two subproblems by setting ((x) + -45.76923077) equal to 24.795614229 and -24.795614229.Subproblem 1
(x) + -45.76923077 = 24.795614229 Simplifying (x) + -45.76923077 = 24.795614229 x + -45.76923077 = 24.795614229 Reorder the terms: -45.76923077 + x = 24.795614229 Solving -45.76923077 + x = 24.795614229 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 = 24.795614229 + 45.76923077 Combine like terms: -45.76923077 + 45.76923077 = 0.00000000 0.00000000 + x = 24.795614229 + 45.76923077 x = 24.795614229 + 45.76923077 Combine like terms: 24.795614229 + 45.76923077 = 70.564844999 x = 70.564844999 Simplifying x = 70.564844999Subproblem 2
(x) + -45.76923077 = -24.795614229 Simplifying (x) + -45.76923077 = -24.795614229 x + -45.76923077 = -24.795614229 Reorder the terms: -45.76923077 + x = -24.795614229 Solving -45.76923077 + x = -24.795614229 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 = -24.795614229 + 45.76923077 Combine like terms: -45.76923077 + 45.76923077 = 0.00000000 0.00000000 + x = -24.795614229 + 45.76923077 x = -24.795614229 + 45.76923077 Combine like terms: -24.795614229 + 45.76923077 = 20.973616541 x = 20.973616541 Simplifying x = 20.973616541Solution
The solution to the problem is based on the solutions from the subproblems. x = {70.564844999, 20.973616541}
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