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Simplifying 9x2 + -25 = 30x + -5 Reorder the terms: -25 + 9x2 = 30x + -5 Reorder the terms: -25 + 9x2 = -5 + 30x Solving -25 + 9x2 = -5 + 30x Solving for variable 'x'. Reorder the terms: -25 + 5 + -30x + 9x2 = -5 + 30x + 5 + -30x Combine like terms: -25 + 5 = -20 -20 + -30x + 9x2 = -5 + 30x + 5 + -30x Reorder the terms: -20 + -30x + 9x2 = -5 + 5 + 30x + -30x Combine like terms: -5 + 5 = 0 -20 + -30x + 9x2 = 0 + 30x + -30x -20 + -30x + 9x2 = 30x + -30x Combine like terms: 30x + -30x = 0 -20 + -30x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -2.222222222 + -3.333333333x + x2 = 0 Move the constant term to the right: Add '2.222222222' to each side of the equation. -2.222222222 + -3.333333333x + 2.222222222 + x2 = 0 + 2.222222222 Reorder the terms: -2.222222222 + 2.222222222 + -3.333333333x + x2 = 0 + 2.222222222 Combine like terms: -2.222222222 + 2.222222222 = 0.000000000 0.000000000 + -3.333333333x + x2 = 0 + 2.222222222 -3.333333333x + x2 = 0 + 2.222222222 Combine like terms: 0 + 2.222222222 = 2.222222222 -3.333333333x + x2 = 2.222222222 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 = 2.222222222 + 2.777777779 Reorder the terms: 2.777777779 + -3.333333333x + x2 = 2.222222222 + 2.777777779 Combine like terms: 2.222222222 + 2.777777779 = 5.000000001 2.777777779 + -3.333333333x + x2 = 5.000000001 Factor a perfect square on the left side: (x + -1.666666667)(x + -1.666666667) = 5.000000001 Calculate the square root of the right side: 2.236067978 Break this problem into two subproblems by setting (x + -1.666666667) equal to 2.236067978 and -2.236067978.Subproblem 1
x + -1.666666667 = 2.236067978 Simplifying x + -1.666666667 = 2.236067978 Reorder the terms: -1.666666667 + x = 2.236067978 Solving -1.666666667 + x = 2.236067978 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 = 2.236067978 + 1.666666667 Combine like terms: -1.666666667 + 1.666666667 = 0.000000000 0.000000000 + x = 2.236067978 + 1.666666667 x = 2.236067978 + 1.666666667 Combine like terms: 2.236067978 + 1.666666667 = 3.902734645 x = 3.902734645 Simplifying x = 3.902734645Subproblem 2
x + -1.666666667 = -2.236067978 Simplifying x + -1.666666667 = -2.236067978 Reorder the terms: -1.666666667 + x = -2.236067978 Solving -1.666666667 + x = -2.236067978 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 = -2.236067978 + 1.666666667 Combine like terms: -1.666666667 + 1.666666667 = 0.000000000 0.000000000 + x = -2.236067978 + 1.666666667 x = -2.236067978 + 1.666666667 Combine like terms: -2.236067978 + 1.666666667 = -0.569401311 x = -0.569401311 Simplifying x = -0.569401311Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.902734645, -0.569401311}
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