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Simplifying 54x2 + -18x + -0.25 = 0 Reorder the terms: -0.25 + -18x + 54x2 = 0 Solving -0.25 + -18x + 54x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 54 the coefficient of the squared term: Divide each side by '54'. -0.00462962963 + -0.3333333333x + x2 = 0 Move the constant term to the right: Add '0.00462962963' to each side of the equation. -0.00462962963 + -0.3333333333x + 0.00462962963 + x2 = 0 + 0.00462962963 Reorder the terms: -0.00462962963 + 0.00462962963 + -0.3333333333x + x2 = 0 + 0.00462962963 Combine like terms: -0.00462962963 + 0.00462962963 = 0.00000000000 0.00000000000 + -0.3333333333x + x2 = 0 + 0.00462962963 -0.3333333333x + x2 = 0 + 0.00462962963 Combine like terms: 0 + 0.00462962963 = 0.00462962963 -0.3333333333x + x2 = 0.00462962963 The x term is -0.3333333333x. Take half its coefficient (-0.1666666667). Square it (0.02777777779) and add it to both sides. Add '0.02777777779' to each side of the equation. -0.3333333333x + 0.02777777779 + x2 = 0.00462962963 + 0.02777777779 Reorder the terms: 0.02777777779 + -0.3333333333x + x2 = 0.00462962963 + 0.02777777779 Combine like terms: 0.00462962963 + 0.02777777779 = 0.03240740742 0.02777777779 + -0.3333333333x + x2 = 0.03240740742 Factor a perfect square on the left side: (x + -0.1666666667)(x + -0.1666666667) = 0.03240740742 Calculate the square root of the right side: 0.180020575 Break this problem into two subproblems by setting (x + -0.1666666667) equal to 0.180020575 and -0.180020575.Subproblem 1
x + -0.1666666667 = 0.180020575 Simplifying x + -0.1666666667 = 0.180020575 Reorder the terms: -0.1666666667 + x = 0.180020575 Solving -0.1666666667 + x = 0.180020575 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1666666667' to each side of the equation. -0.1666666667 + 0.1666666667 + x = 0.180020575 + 0.1666666667 Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000 0.0000000000 + x = 0.180020575 + 0.1666666667 x = 0.180020575 + 0.1666666667 Combine like terms: 0.180020575 + 0.1666666667 = 0.3466872417 x = 0.3466872417 Simplifying x = 0.3466872417Subproblem 2
x + -0.1666666667 = -0.180020575 Simplifying x + -0.1666666667 = -0.180020575 Reorder the terms: -0.1666666667 + x = -0.180020575 Solving -0.1666666667 + x = -0.180020575 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1666666667' to each side of the equation. -0.1666666667 + 0.1666666667 + x = -0.180020575 + 0.1666666667 Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000 0.0000000000 + x = -0.180020575 + 0.1666666667 x = -0.180020575 + 0.1666666667 Combine like terms: -0.180020575 + 0.1666666667 = -0.0133539083 x = -0.0133539083 Simplifying x = -0.0133539083Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.3466872417, -0.0133539083}
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