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Simplifying 3X2 + -80X + 90 = 0 Reorder the terms: 90 + -80X + 3X2 = 0 Solving 90 + -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'. 30 + -26.66666667X + X2 = 0 Move the constant term to the right: Add '-30' to each side of the equation. 30 + -26.66666667X + -30 + X2 = 0 + -30 Reorder the terms: 30 + -30 + -26.66666667X + X2 = 0 + -30 Combine like terms: 30 + -30 = 0 0 + -26.66666667X + X2 = 0 + -30 -26.66666667X + X2 = 0 + -30 Combine like terms: 0 + -30 = -30 -26.66666667X + X2 = -30 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 = -30 + 177.7777780 Reorder the terms: 177.7777780 + -26.66666667X + X2 = -30 + 177.7777780 Combine like terms: -30 + 177.7777780 = 147.777778 177.7777780 + -26.66666667X + X2 = 147.777778 Factor a perfect square on the left side: (X + -13.33333334)(X + -13.33333334) = 147.777778 Calculate the square root of the right side: 12.156388362 Break this problem into two subproblems by setting (X + -13.33333334) equal to 12.156388362 and -12.156388362.Subproblem 1
X + -13.33333334 = 12.156388362 Simplifying X + -13.33333334 = 12.156388362 Reorder the terms: -13.33333334 + X = 12.156388362 Solving -13.33333334 + X = 12.156388362 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 = 12.156388362 + 13.33333334 Combine like terms: -13.33333334 + 13.33333334 = 0.00000000 0.00000000 + X = 12.156388362 + 13.33333334 X = 12.156388362 + 13.33333334 Combine like terms: 12.156388362 + 13.33333334 = 25.489721702 X = 25.489721702 Simplifying X = 25.489721702Subproblem 2
X + -13.33333334 = -12.156388362 Simplifying X + -13.33333334 = -12.156388362 Reorder the terms: -13.33333334 + X = -12.156388362 Solving -13.33333334 + X = -12.156388362 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 = -12.156388362 + 13.33333334 Combine like terms: -13.33333334 + 13.33333334 = 0.00000000 0.00000000 + X = -12.156388362 + 13.33333334 X = -12.156388362 + 13.33333334 Combine like terms: -12.156388362 + 13.33333334 = 1.176944978 X = 1.176944978 Simplifying X = 1.176944978Solution
The solution to the problem is based on the solutions from the subproblems. X = {25.489721702, 1.176944978}
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