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Simplifying 9x(x + -4) = 9x + -37 Reorder the terms: 9x(-4 + x) = 9x + -37 (-4 * 9x + x * 9x) = 9x + -37 (-36x + 9x2) = 9x + -37 Reorder the terms: -36x + 9x2 = -37 + 9x Solving -36x + 9x2 = -37 + 9x Solving for variable 'x'. Reorder the terms: 37 + -36x + -9x + 9x2 = -37 + 9x + 37 + -9x Combine like terms: -36x + -9x = -45x 37 + -45x + 9x2 = -37 + 9x + 37 + -9x Reorder the terms: 37 + -45x + 9x2 = -37 + 37 + 9x + -9x Combine like terms: -37 + 37 = 0 37 + -45x + 9x2 = 0 + 9x + -9x 37 + -45x + 9x2 = 9x + -9x Combine like terms: 9x + -9x = 0 37 + -45x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 4.111111111 + -5x + x2 = 0 Move the constant term to the right: Add '-4.111111111' to each side of the equation. 4.111111111 + -5x + -4.111111111 + x2 = 0 + -4.111111111 Reorder the terms: 4.111111111 + -4.111111111 + -5x + x2 = 0 + -4.111111111 Combine like terms: 4.111111111 + -4.111111111 = 0.000000000 0.000000000 + -5x + x2 = 0 + -4.111111111 -5x + x2 = 0 + -4.111111111 Combine like terms: 0 + -4.111111111 = -4.111111111 -5x + x2 = -4.111111111 The x term is -5x. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5x + 6.25 + x2 = -4.111111111 + 6.25 Reorder the terms: 6.25 + -5x + x2 = -4.111111111 + 6.25 Combine like terms: -4.111111111 + 6.25 = 2.138888889 6.25 + -5x + x2 = 2.138888889 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 2.138888889 Calculate the square root of the right side: 1.462494065 Break this problem into two subproblems by setting (x + -2.5) equal to 1.462494065 and -1.462494065.Subproblem 1
x + -2.5 = 1.462494065 Simplifying x + -2.5 = 1.462494065 Reorder the terms: -2.5 + x = 1.462494065 Solving -2.5 + x = 1.462494065 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = 1.462494065 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 1.462494065 + 2.5 x = 1.462494065 + 2.5 Combine like terms: 1.462494065 + 2.5 = 3.962494065 x = 3.962494065 Simplifying x = 3.962494065Subproblem 2
x + -2.5 = -1.462494065 Simplifying x + -2.5 = -1.462494065 Reorder the terms: -2.5 + x = -1.462494065 Solving -2.5 + x = -1.462494065 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = -1.462494065 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -1.462494065 + 2.5 x = -1.462494065 + 2.5 Combine like terms: -1.462494065 + 2.5 = 1.037505935 x = 1.037505935 Simplifying x = 1.037505935Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.962494065, 1.037505935}
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