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Simplifying 3X2 + -80X + 230 = 0 Reorder the terms: 230 + -80X + 3X2 = 0 Solving 230 + -80X + 3X2 = 0 Solving for variable 'X'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 76.66666667 + -26.66666667X + X2 = 0 Move the constant term to the right: Add '-76.66666667' to each side of the equation. 76.66666667 + -26.66666667X + -76.66666667 + X2 = 0 + -76.66666667 Reorder the terms: 76.66666667 + -76.66666667 + -26.66666667X + X2 = 0 + -76.66666667 Combine like terms: 76.66666667 + -76.66666667 = 0.00000000 0.00000000 + -26.66666667X + X2 = 0 + -76.66666667 -26.66666667X + X2 = 0 + -76.66666667 Combine like terms: 0 + -76.66666667 = -76.66666667 -26.66666667X + X2 = -76.66666667 The X term is -26.66666667X. Take half its coefficient (-13.33333334). Square it (177.7777780) and add it to both sides. Add '177.7777780' to each side of the equation. -26.66666667X + 177.7777780 + X2 = -76.66666667 + 177.7777780 Reorder the terms: 177.7777780 + -26.66666667X + X2 = -76.66666667 + 177.7777780 Combine like terms: -76.66666667 + 177.7777780 = 101.11111133 177.7777780 + -26.66666667X + X2 = 101.11111133 Factor a perfect square on the left side: (X + -13.33333334)(X + -13.33333334) = 101.11111133 Calculate the square root of the right side: 10.055402097 Break this problem into two subproblems by setting (X + -13.33333334) equal to 10.055402097 and -10.055402097.Subproblem 1
X + -13.33333334 = 10.055402097 Simplifying X + -13.33333334 = 10.055402097 Reorder the terms: -13.33333334 + X = 10.055402097 Solving -13.33333334 + X = 10.055402097 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '13.33333334' to each side of the equation. -13.33333334 + 13.33333334 + X = 10.055402097 + 13.33333334 Combine like terms: -13.33333334 + 13.33333334 = 0.00000000 0.00000000 + X = 10.055402097 + 13.33333334 X = 10.055402097 + 13.33333334 Combine like terms: 10.055402097 + 13.33333334 = 23.388735437 X = 23.388735437 Simplifying X = 23.388735437Subproblem 2
X + -13.33333334 = -10.055402097 Simplifying X + -13.33333334 = -10.055402097 Reorder the terms: -13.33333334 + X = -10.055402097 Solving -13.33333334 + X = -10.055402097 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '13.33333334' to each side of the equation. -13.33333334 + 13.33333334 + X = -10.055402097 + 13.33333334 Combine like terms: -13.33333334 + 13.33333334 = 0.00000000 0.00000000 + X = -10.055402097 + 13.33333334 X = -10.055402097 + 13.33333334 Combine like terms: -10.055402097 + 13.33333334 = 3.277931243 X = 3.277931243 Simplifying X = 3.277931243Solution
The solution to the problem is based on the solutions from the subproblems. X = {23.388735437, 3.277931243}
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