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Simplifying 100 = 0.013x2 + -1.19x + 28.24 Reorder the terms: 100 = 28.24 + -1.19x + 0.013x2 Solving 100 = 28.24 + -1.19x + 0.013x2 Solving for variable 'x'. Combine like terms: 100 + -28.24 = 71.76 71.76 + 1.19x + -0.013x2 = 28.24 + -1.19x + 0.013x2 + -28.24 + 1.19x + -0.013x2 Reorder the terms: 71.76 + 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 71.76 + 1.19x + -0.013x2 = 0.00 + -1.19x + 1.19x + 0.013x2 + -0.013x2 71.76 + 1.19x + -0.013x2 = -1.19x + 1.19x + 0.013x2 + -0.013x2 Combine like terms: -1.19x + 1.19x = 0.00 71.76 + 1.19x + -0.013x2 = 0.00 + 0.013x2 + -0.013x2 71.76 + 1.19x + -0.013x2 = 0.013x2 + -0.013x2 Combine like terms: 0.013x2 + -0.013x2 = 0.000 71.76 + 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'. -5520 + -91.53846154x + x2 = 0 Move the constant term to the right: Add '5520' to each side of the equation. -5520 + -91.53846154x + 5520 + x2 = 0 + 5520 Reorder the terms: -5520 + 5520 + -91.53846154x + x2 = 0 + 5520 Combine like terms: -5520 + 5520 = 0 0 + -91.53846154x + x2 = 0 + 5520 -91.53846154x + x2 = 0 + 5520 Combine like terms: 0 + 5520 = 5520 -91.53846154x + x2 = 5520 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 = 5520 + 2094.822485 Reorder the terms: 2094.822485 + -91.53846154x + x2 = 5520 + 2094.822485 Combine like terms: 5520 + 2094.822485 = 7614.822485 2094.822485 + -91.53846154x + x2 = 7614.822485 Factor a perfect square on the left side: (x + -45.76923077)(x + -45.76923077) = 7614.822485 Calculate the square root of the right side: 87.262950242 Break this problem into two subproblems by setting (x + -45.76923077) equal to 87.262950242 and -87.262950242.Subproblem 1
x + -45.76923077 = 87.262950242 Simplifying x + -45.76923077 = 87.262950242 Reorder the terms: -45.76923077 + x = 87.262950242 Solving -45.76923077 + x = 87.262950242 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 = 87.262950242 + 45.76923077 Combine like terms: -45.76923077 + 45.76923077 = 0.00000000 0.00000000 + x = 87.262950242 + 45.76923077 x = 87.262950242 + 45.76923077 Combine like terms: 87.262950242 + 45.76923077 = 133.032181012 x = 133.032181012 Simplifying x = 133.032181012Subproblem 2
x + -45.76923077 = -87.262950242 Simplifying x + -45.76923077 = -87.262950242 Reorder the terms: -45.76923077 + x = -87.262950242 Solving -45.76923077 + x = -87.262950242 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 = -87.262950242 + 45.76923077 Combine like terms: -45.76923077 + 45.76923077 = 0.00000000 0.00000000 + x = -87.262950242 + 45.76923077 x = -87.262950242 + 45.76923077 Combine like terms: -87.262950242 + 45.76923077 = -41.493719472 x = -41.493719472 Simplifying x = -41.493719472Solution
The solution to the problem is based on the solutions from the subproblems. x = {133.032181012, -41.493719472}
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