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Simplifying 6x(x + -9) + -5 = 0 Reorder the terms: 6x(-9 + x) + -5 = 0 (-9 * 6x + x * 6x) + -5 = 0 (-54x + 6x2) + -5 = 0 Reorder the terms: -5 + -54x + 6x2 = 0 Solving -5 + -54x + 6x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -0.8333333333 + -9x + x2 = 0 Move the constant term to the right: Add '0.8333333333' to each side of the equation. -0.8333333333 + -9x + 0.8333333333 + x2 = 0 + 0.8333333333 Reorder the terms: -0.8333333333 + 0.8333333333 + -9x + x2 = 0 + 0.8333333333 Combine like terms: -0.8333333333 + 0.8333333333 = 0.0000000000 0.0000000000 + -9x + x2 = 0 + 0.8333333333 -9x + x2 = 0 + 0.8333333333 Combine like terms: 0 + 0.8333333333 = 0.8333333333 -9x + x2 = 0.8333333333 The x term is -9x. Take half its coefficient (-4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. -9x + 20.25 + x2 = 0.8333333333 + 20.25 Reorder the terms: 20.25 + -9x + x2 = 0.8333333333 + 20.25 Combine like terms: 0.8333333333 + 20.25 = 21.0833333333 20.25 + -9x + x2 = 21.0833333333 Factor a perfect square on the left side: (x + -4.5)(x + -4.5) = 21.0833333333 Calculate the square root of the right side: 4.591659105 Break this problem into two subproblems by setting (x + -4.5) equal to 4.591659105 and -4.591659105.Subproblem 1
x + -4.5 = 4.591659105 Simplifying x + -4.5 = 4.591659105 Reorder the terms: -4.5 + x = 4.591659105 Solving -4.5 + x = 4.591659105 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x = 4.591659105 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = 4.591659105 + 4.5 x = 4.591659105 + 4.5 Combine like terms: 4.591659105 + 4.5 = 9.091659105 x = 9.091659105 Simplifying x = 9.091659105Subproblem 2
x + -4.5 = -4.591659105 Simplifying x + -4.5 = -4.591659105 Reorder the terms: -4.5 + x = -4.591659105 Solving -4.5 + x = -4.591659105 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x = -4.591659105 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = -4.591659105 + 4.5 x = -4.591659105 + 4.5 Combine like terms: -4.591659105 + 4.5 = -0.091659105 x = -0.091659105 Simplifying x = -0.091659105Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.091659105, -0.091659105}
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