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Simplifying 3x2 + -144x + 35 = 0 Reorder the terms: 35 + -144x + 3x2 = 0 Solving 35 + -144x + 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'. 11.66666667 + -48x + x2 = 0 Move the constant term to the right: Add '-11.66666667' to each side of the equation. 11.66666667 + -48x + -11.66666667 + x2 = 0 + -11.66666667 Reorder the terms: 11.66666667 + -11.66666667 + -48x + x2 = 0 + -11.66666667 Combine like terms: 11.66666667 + -11.66666667 = 0.00000000 0.00000000 + -48x + x2 = 0 + -11.66666667 -48x + x2 = 0 + -11.66666667 Combine like terms: 0 + -11.66666667 = -11.66666667 -48x + x2 = -11.66666667 The x term is -48x. Take half its coefficient (-24). Square it (576) and add it to both sides. Add '576' to each side of the equation. -48x + 576 + x2 = -11.66666667 + 576 Reorder the terms: 576 + -48x + x2 = -11.66666667 + 576 Combine like terms: -11.66666667 + 576 = 564.33333333 576 + -48x + x2 = 564.33333333 Factor a perfect square on the left side: (x + -24)(x + -24) = 564.33333333 Calculate the square root of the right side: 23.75570107 Break this problem into two subproblems by setting (x + -24) equal to 23.75570107 and -23.75570107.Subproblem 1
x + -24 = 23.75570107 Simplifying x + -24 = 23.75570107 Reorder the terms: -24 + x = 23.75570107 Solving -24 + x = 23.75570107 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '24' to each side of the equation. -24 + 24 + x = 23.75570107 + 24 Combine like terms: -24 + 24 = 0 0 + x = 23.75570107 + 24 x = 23.75570107 + 24 Combine like terms: 23.75570107 + 24 = 47.75570107 x = 47.75570107 Simplifying x = 47.75570107Subproblem 2
x + -24 = -23.75570107 Simplifying x + -24 = -23.75570107 Reorder the terms: -24 + x = -23.75570107 Solving -24 + x = -23.75570107 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '24' to each side of the equation. -24 + 24 + x = -23.75570107 + 24 Combine like terms: -24 + 24 = 0 0 + x = -23.75570107 + 24 x = -23.75570107 + 24 Combine like terms: -23.75570107 + 24 = 0.24429893 x = 0.24429893 Simplifying x = 0.24429893Solution
The solution to the problem is based on the solutions from the subproblems. x = {47.75570107, 0.24429893}
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