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Simplifying 5x2 = 48x + 27 Reorder the terms: 5x2 = 27 + 48x Solving 5x2 = 27 + 48x Solving for variable 'x'. Reorder the terms: -27 + -48x + 5x2 = 27 + 48x + -27 + -48x Reorder the terms: -27 + -48x + 5x2 = 27 + -27 + 48x + -48x Combine like terms: 27 + -27 = 0 -27 + -48x + 5x2 = 0 + 48x + -48x -27 + -48x + 5x2 = 48x + -48x Combine like terms: 48x + -48x = 0 -27 + -48x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -5.4 + -9.6x + x2 = 0 Move the constant term to the right: Add '5.4' to each side of the equation. -5.4 + -9.6x + 5.4 + x2 = 0 + 5.4 Reorder the terms: -5.4 + 5.4 + -9.6x + x2 = 0 + 5.4 Combine like terms: -5.4 + 5.4 = 0.0 0.0 + -9.6x + x2 = 0 + 5.4 -9.6x + x2 = 0 + 5.4 Combine like terms: 0 + 5.4 = 5.4 -9.6x + x2 = 5.4 The x term is -9.6x. Take half its coefficient (-4.8). Square it (23.04) and add it to both sides. Add '23.04' to each side of the equation. -9.6x + 23.04 + x2 = 5.4 + 23.04 Reorder the terms: 23.04 + -9.6x + x2 = 5.4 + 23.04 Combine like terms: 5.4 + 23.04 = 28.44 23.04 + -9.6x + x2 = 28.44 Factor a perfect square on the left side: (x + -4.8)(x + -4.8) = 28.44 Calculate the square root of the right side: 5.33291665 Break this problem into two subproblems by setting (x + -4.8) equal to 5.33291665 and -5.33291665.Subproblem 1
x + -4.8 = 5.33291665 Simplifying x + -4.8 = 5.33291665 Reorder the terms: -4.8 + x = 5.33291665 Solving -4.8 + x = 5.33291665 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.8' to each side of the equation. -4.8 + 4.8 + x = 5.33291665 + 4.8 Combine like terms: -4.8 + 4.8 = 0.0 0.0 + x = 5.33291665 + 4.8 x = 5.33291665 + 4.8 Combine like terms: 5.33291665 + 4.8 = 10.13291665 x = 10.13291665 Simplifying x = 10.13291665Subproblem 2
x + -4.8 = -5.33291665 Simplifying x + -4.8 = -5.33291665 Reorder the terms: -4.8 + x = -5.33291665 Solving -4.8 + x = -5.33291665 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.8' to each side of the equation. -4.8 + 4.8 + x = -5.33291665 + 4.8 Combine like terms: -4.8 + 4.8 = 0.0 0.0 + x = -5.33291665 + 4.8 x = -5.33291665 + 4.8 Combine like terms: -5.33291665 + 4.8 = -0.53291665 x = -0.53291665 Simplifying x = -0.53291665Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.13291665, -0.53291665}
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