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Simplifying 15x2 + -44x + 30 = 0 Reorder the terms: 30 + -44x + 15x2 = 0 Solving 30 + -44x + 15x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 15 the coefficient of the squared term: Divide each side by '15'. 2 + -2.933333333x + x2 = 0 Move the constant term to the right: Add '-2' to each side of the equation. 2 + -2.933333333x + -2 + x2 = 0 + -2 Reorder the terms: 2 + -2 + -2.933333333x + x2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -2.933333333x + x2 = 0 + -2 -2.933333333x + x2 = 0 + -2 Combine like terms: 0 + -2 = -2 -2.933333333x + x2 = -2 The x term is -2.933333333x. Take half its coefficient (-1.466666667). Square it (2.151111112) and add it to both sides. Add '2.151111112' to each side of the equation. -2.933333333x + 2.151111112 + x2 = -2 + 2.151111112 Reorder the terms: 2.151111112 + -2.933333333x + x2 = -2 + 2.151111112 Combine like terms: -2 + 2.151111112 = 0.151111112 2.151111112 + -2.933333333x + x2 = 0.151111112 Factor a perfect square on the left side: (x + -1.466666667)(x + -1.466666667) = 0.151111112 Calculate the square root of the right side: 0.388730127 Break this problem into two subproblems by setting (x + -1.466666667) equal to 0.388730127 and -0.388730127.Subproblem 1
x + -1.466666667 = 0.388730127 Simplifying x + -1.466666667 = 0.388730127 Reorder the terms: -1.466666667 + x = 0.388730127 Solving -1.466666667 + x = 0.388730127 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.466666667' to each side of the equation. -1.466666667 + 1.466666667 + x = 0.388730127 + 1.466666667 Combine like terms: -1.466666667 + 1.466666667 = 0.000000000 0.000000000 + x = 0.388730127 + 1.466666667 x = 0.388730127 + 1.466666667 Combine like terms: 0.388730127 + 1.466666667 = 1.855396794 x = 1.855396794 Simplifying x = 1.855396794Subproblem 2
x + -1.466666667 = -0.388730127 Simplifying x + -1.466666667 = -0.388730127 Reorder the terms: -1.466666667 + x = -0.388730127 Solving -1.466666667 + x = -0.388730127 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.466666667' to each side of the equation. -1.466666667 + 1.466666667 + x = -0.388730127 + 1.466666667 Combine like terms: -1.466666667 + 1.466666667 = 0.000000000 0.000000000 + x = -0.388730127 + 1.466666667 x = -0.388730127 + 1.466666667 Combine like terms: -0.388730127 + 1.466666667 = 1.07793654 x = 1.07793654 Simplifying x = 1.07793654Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.855396794, 1.07793654}
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