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Simplifying 9x(x + 4) = 5 Reorder the terms: 9x(4 + x) = 5 (4 * 9x + x * 9x) = 5 (36x + 9x2) = 5 Solving 36x + 9x2 = 5 Solving for variable 'x'. Reorder the terms: -5 + 36x + 9x2 = 5 + -5 Combine like terms: 5 + -5 = 0 -5 + 36x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -0.5555555556 + 4x + x2 = 0 Move the constant term to the right: Add '0.5555555556' to each side of the equation. -0.5555555556 + 4x + 0.5555555556 + x2 = 0 + 0.5555555556 Reorder the terms: -0.5555555556 + 0.5555555556 + 4x + x2 = 0 + 0.5555555556 Combine like terms: -0.5555555556 + 0.5555555556 = 0.0000000000 0.0000000000 + 4x + x2 = 0 + 0.5555555556 4x + x2 = 0 + 0.5555555556 Combine like terms: 0 + 0.5555555556 = 0.5555555556 4x + x2 = 0.5555555556 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = 0.5555555556 + 4 Reorder the terms: 4 + 4x + x2 = 0.5555555556 + 4 Combine like terms: 0.5555555556 + 4 = 4.5555555556 4 + 4x + x2 = 4.5555555556 Factor a perfect square on the left side: (x + 2)(x + 2) = 4.5555555556 Calculate the square root of the right side: 2.134374746 Break this problem into two subproblems by setting (x + 2) equal to 2.134374746 and -2.134374746.Subproblem 1
x + 2 = 2.134374746 Simplifying x + 2 = 2.134374746 Reorder the terms: 2 + x = 2.134374746 Solving 2 + x = 2.134374746 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 2.134374746 + -2 Combine like terms: 2 + -2 = 0 0 + x = 2.134374746 + -2 x = 2.134374746 + -2 Combine like terms: 2.134374746 + -2 = 0.134374746 x = 0.134374746 Simplifying x = 0.134374746Subproblem 2
x + 2 = -2.134374746 Simplifying x + 2 = -2.134374746 Reorder the terms: 2 + x = -2.134374746 Solving 2 + x = -2.134374746 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -2.134374746 + -2 Combine like terms: 2 + -2 = 0 0 + x = -2.134374746 + -2 x = -2.134374746 + -2 Combine like terms: -2.134374746 + -2 = -4.134374746 x = -4.134374746 Simplifying x = -4.134374746Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.134374746, -4.134374746}
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