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Simplifying 25 = 0.013x2 + -1.19x + 28.24 Reorder the terms: 25 = 28.24 + -1.19x + 0.013x2 Solving 25 = 28.24 + -1.19x + 0.013x2 Solving for variable 'x'. Combine like terms: 25 + -28.24 = -3.24 -3.24 + 1.19x + -0.013x2 = 28.24 + -1.19x + 0.013x2 + -28.24 + 1.19x + -0.013x2 Reorder the terms: -3.24 + 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 -3.24 + 1.19x + -0.013x2 = 0.00 + -1.19x + 1.19x + 0.013x2 + -0.013x2 -3.24 + 1.19x + -0.013x2 = -1.19x + 1.19x + 0.013x2 + -0.013x2 Combine like terms: -1.19x + 1.19x = 0.00 -3.24 + 1.19x + -0.013x2 = 0.00 + 0.013x2 + -0.013x2 -3.24 + 1.19x + -0.013x2 = 0.013x2 + -0.013x2 Combine like terms: 0.013x2 + -0.013x2 = 0.000 -3.24 + 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'. 249.2307692 + -91.53846154x + x2 = 0 Move the constant term to the right: Add '-249.2307692' to each side of the equation. 249.2307692 + -91.53846154x + -249.2307692 + x2 = 0 + -249.2307692 Reorder the terms: 249.2307692 + -249.2307692 + -91.53846154x + x2 = 0 + -249.2307692 Combine like terms: 249.2307692 + -249.2307692 = 0.0000000 0.0000000 + -91.53846154x + x2 = 0 + -249.2307692 -91.53846154x + x2 = 0 + -249.2307692 Combine like terms: 0 + -249.2307692 = -249.2307692 -91.53846154x + x2 = -249.2307692 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 = -249.2307692 + 2094.822485 Reorder the terms: 2094.822485 + -91.53846154x + x2 = -249.2307692 + 2094.822485 Combine like terms: -249.2307692 + 2094.822485 = 1845.5917158 2094.822485 + -91.53846154x + x2 = 1845.5917158 Factor a perfect square on the left side: (x + -45.76923077)(x + -45.76923077) = 1845.5917158 Calculate the square root of the right side: 42.960350508 Break this problem into two subproblems by setting (x + -45.76923077) equal to 42.960350508 and -42.960350508.Subproblem 1
x + -45.76923077 = 42.960350508 Simplifying x + -45.76923077 = 42.960350508 Reorder the terms: -45.76923077 + x = 42.960350508 Solving -45.76923077 + x = 42.960350508 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 = 42.960350508 + 45.76923077 Combine like terms: -45.76923077 + 45.76923077 = 0.00000000 0.00000000 + x = 42.960350508 + 45.76923077 x = 42.960350508 + 45.76923077 Combine like terms: 42.960350508 + 45.76923077 = 88.729581278 x = 88.729581278 Simplifying x = 88.729581278Subproblem 2
x + -45.76923077 = -42.960350508 Simplifying x + -45.76923077 = -42.960350508 Reorder the terms: -45.76923077 + x = -42.960350508 Solving -45.76923077 + x = -42.960350508 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 = -42.960350508 + 45.76923077 Combine like terms: -45.76923077 + 45.76923077 = 0.00000000 0.00000000 + x = -42.960350508 + 45.76923077 x = -42.960350508 + 45.76923077 Combine like terms: -42.960350508 + 45.76923077 = 2.808880262 x = 2.808880262 Simplifying x = 2.808880262Solution
The solution to the problem is based on the solutions from the subproblems. x = {88.729581278, 2.808880262}
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