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Simplifying 9x2 + -30x + 2.25 = 0 Reorder the terms: 2.25 + -30x + 9x2 = 0 Solving 2.25 + -30x + 9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 0.25 + -3.333333333x + x2 = 0 Move the constant term to the right: Add '-0.25' to each side of the equation. 0.25 + -3.333333333x + -0.25 + x2 = 0 + -0.25 Reorder the terms: 0.25 + -0.25 + -3.333333333x + x2 = 0 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + -3.333333333x + x2 = 0 + -0.25 -3.333333333x + x2 = 0 + -0.25 Combine like terms: 0 + -0.25 = -0.25 -3.333333333x + x2 = -0.25 The x term is -3.333333333x. Take half its coefficient (-1.666666667). Square it (2.777777779) and add it to both sides. Add '2.777777779' to each side of the equation. -3.333333333x + 2.777777779 + x2 = -0.25 + 2.777777779 Reorder the terms: 2.777777779 + -3.333333333x + x2 = -0.25 + 2.777777779 Combine like terms: -0.25 + 2.777777779 = 2.527777779 2.777777779 + -3.333333333x + x2 = 2.527777779 Factor a perfect square on the left side: (x + -1.666666667)(x + -1.666666667) = 2.527777779 Calculate the square root of the right side: 1.589898669 Break this problem into two subproblems by setting (x + -1.666666667) equal to 1.589898669 and -1.589898669.Subproblem 1
x + -1.666666667 = 1.589898669 Simplifying x + -1.666666667 = 1.589898669 Reorder the terms: -1.666666667 + x = 1.589898669 Solving -1.666666667 + x = 1.589898669 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.666666667' to each side of the equation. -1.666666667 + 1.666666667 + x = 1.589898669 + 1.666666667 Combine like terms: -1.666666667 + 1.666666667 = 0.000000000 0.000000000 + x = 1.589898669 + 1.666666667 x = 1.589898669 + 1.666666667 Combine like terms: 1.589898669 + 1.666666667 = 3.256565336 x = 3.256565336 Simplifying x = 3.256565336Subproblem 2
x + -1.666666667 = -1.589898669 Simplifying x + -1.666666667 = -1.589898669 Reorder the terms: -1.666666667 + x = -1.589898669 Solving -1.666666667 + x = -1.589898669 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.666666667' to each side of the equation. -1.666666667 + 1.666666667 + x = -1.589898669 + 1.666666667 Combine like terms: -1.666666667 + 1.666666667 = 0.000000000 0.000000000 + x = -1.589898669 + 1.666666667 x = -1.589898669 + 1.666666667 Combine like terms: -1.589898669 + 1.666666667 = 0.076767998 x = 0.076767998 Simplifying x = 0.076767998Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.256565336, 0.076767998}
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