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Simplifying 6x2 + -54x = 5x2 + -6x + -36 Reorder the terms: -54x + 6x2 = 5x2 + -6x + -36 Reorder the terms: -54x + 6x2 = -36 + -6x + 5x2 Solving -54x + 6x2 = -36 + -6x + 5x2 Solving for variable 'x'. Reorder the terms: 36 + -54x + 6x + 6x2 + -5x2 = -36 + -6x + 5x2 + 36 + 6x + -5x2 Combine like terms: -54x + 6x = -48x 36 + -48x + 6x2 + -5x2 = -36 + -6x + 5x2 + 36 + 6x + -5x2 Combine like terms: 6x2 + -5x2 = 1x2 36 + -48x + 1x2 = -36 + -6x + 5x2 + 36 + 6x + -5x2 Reorder the terms: 36 + -48x + 1x2 = -36 + 36 + -6x + 6x + 5x2 + -5x2 Combine like terms: -36 + 36 = 0 36 + -48x + 1x2 = 0 + -6x + 6x + 5x2 + -5x2 36 + -48x + 1x2 = -6x + 6x + 5x2 + -5x2 Combine like terms: -6x + 6x = 0 36 + -48x + 1x2 = 0 + 5x2 + -5x2 36 + -48x + 1x2 = 5x2 + -5x2 Combine like terms: 5x2 + -5x2 = 0 36 + -48x + 1x2 = 0 Begin completing the square. Move the constant term to the right: Add '-36' to each side of the equation. 36 + -48x + -36 + x2 = 0 + -36 Reorder the terms: 36 + -36 + -48x + x2 = 0 + -36 Combine like terms: 36 + -36 = 0 0 + -48x + x2 = 0 + -36 -48x + x2 = 0 + -36 Combine like terms: 0 + -36 = -36 -48x + x2 = -36 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 = -36 + 576 Reorder the terms: 576 + -48x + x2 = -36 + 576 Combine like terms: -36 + 576 = 540 576 + -48x + x2 = 540 Factor a perfect square on the left side: (x + -24)(x + -24) = 540 Calculate the square root of the right side: 23.237900077 Break this problem into two subproblems by setting (x + -24) equal to 23.237900077 and -23.237900077.Subproblem 1
x + -24 = 23.237900077 Simplifying x + -24 = 23.237900077 Reorder the terms: -24 + x = 23.237900077 Solving -24 + x = 23.237900077 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 = 23.237900077 + 24 Combine like terms: -24 + 24 = 0 0 + x = 23.237900077 + 24 x = 23.237900077 + 24 Combine like terms: 23.237900077 + 24 = 47.237900077 x = 47.237900077 Simplifying x = 47.237900077Subproblem 2
x + -24 = -23.237900077 Simplifying x + -24 = -23.237900077 Reorder the terms: -24 + x = -23.237900077 Solving -24 + x = -23.237900077 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 = -23.237900077 + 24 Combine like terms: -24 + 24 = 0 0 + x = -23.237900077 + 24 x = -23.237900077 + 24 Combine like terms: -23.237900077 + 24 = 0.762099923 x = 0.762099923 Simplifying x = 0.762099923Solution
The solution to the problem is based on the solutions from the subproblems. x = {47.237900077, 0.762099923}
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