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Simplifying 45X2 + -26X + 5 = 30 Reorder the terms: 5 + -26X + 45X2 = 30 Solving 5 + -26X + 45X2 = 30 Solving for variable 'X'. Reorder the terms: 5 + -30 + -26X + 45X2 = 30 + -30 Combine like terms: 5 + -30 = -25 -25 + -26X + 45X2 = 30 + -30 Combine like terms: 30 + -30 = 0 -25 + -26X + 45X2 = 0 Begin completing the square. Divide all terms by 45 the coefficient of the squared term: Divide each side by '45'. -0.5555555556 + -0.5777777778X + X2 = 0 Move the constant term to the right: Add '0.5555555556' to each side of the equation. -0.5555555556 + -0.5777777778X + 0.5555555556 + X2 = 0 + 0.5555555556 Reorder the terms: -0.5555555556 + 0.5555555556 + -0.5777777778X + X2 = 0 + 0.5555555556 Combine like terms: -0.5555555556 + 0.5555555556 = 0.0000000000 0.0000000000 + -0.5777777778X + X2 = 0 + 0.5555555556 -0.5777777778X + X2 = 0 + 0.5555555556 Combine like terms: 0 + 0.5555555556 = 0.5555555556 -0.5777777778X + X2 = 0.5555555556 The X term is -0.5777777778X. Take half its coefficient (-0.2888888889). Square it (0.08345679013) and add it to both sides. Add '0.08345679013' to each side of the equation. -0.5777777778X + 0.08345679013 + X2 = 0.5555555556 + 0.08345679013 Reorder the terms: 0.08345679013 + -0.5777777778X + X2 = 0.5555555556 + 0.08345679013 Combine like terms: 0.5555555556 + 0.08345679013 = 0.63901234573 0.08345679013 + -0.5777777778X + X2 = 0.63901234573 Factor a perfect square on the left side: (X + -0.2888888889)(X + -0.2888888889) = 0.63901234573 Calculate the square root of the right side: 0.799382478 Break this problem into two subproblems by setting (X + -0.2888888889) equal to 0.799382478 and -0.799382478.Subproblem 1
X + -0.2888888889 = 0.799382478 Simplifying X + -0.2888888889 = 0.799382478 Reorder the terms: -0.2888888889 + X = 0.799382478 Solving -0.2888888889 + X = 0.799382478 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '0.2888888889' to each side of the equation. -0.2888888889 + 0.2888888889 + X = 0.799382478 + 0.2888888889 Combine like terms: -0.2888888889 + 0.2888888889 = 0.0000000000 0.0000000000 + X = 0.799382478 + 0.2888888889 X = 0.799382478 + 0.2888888889 Combine like terms: 0.799382478 + 0.2888888889 = 1.0882713669 X = 1.0882713669 Simplifying X = 1.0882713669Subproblem 2
X + -0.2888888889 = -0.799382478 Simplifying X + -0.2888888889 = -0.799382478 Reorder the terms: -0.2888888889 + X = -0.799382478 Solving -0.2888888889 + X = -0.799382478 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '0.2888888889' to each side of the equation. -0.2888888889 + 0.2888888889 + X = -0.799382478 + 0.2888888889 Combine like terms: -0.2888888889 + 0.2888888889 = 0.0000000000 0.0000000000 + X = -0.799382478 + 0.2888888889 X = -0.799382478 + 0.2888888889 Combine like terms: -0.799382478 + 0.2888888889 = -0.5104935891 X = -0.5104935891 Simplifying X = -0.5104935891Solution
The solution to the problem is based on the solutions from the subproblems. X = {1.0882713669, -0.5104935891}
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