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Simplifying 5x2 + 24x + -540 = 0 Reorder the terms: -540 + 24x + 5x2 = 0 Solving -540 + 24x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -108 + 4.8x + x2 = 0 Move the constant term to the right: Add '108' to each side of the equation. -108 + 4.8x + 108 + x2 = 0 + 108 Reorder the terms: -108 + 108 + 4.8x + x2 = 0 + 108 Combine like terms: -108 + 108 = 0 0 + 4.8x + x2 = 0 + 108 4.8x + x2 = 0 + 108 Combine like terms: 0 + 108 = 108 4.8x + x2 = 108 The x term is 4.8x. Take half its coefficient (2.4). Square it (5.76) and add it to both sides. Add '5.76' to each side of the equation. 4.8x + 5.76 + x2 = 108 + 5.76 Reorder the terms: 5.76 + 4.8x + x2 = 108 + 5.76 Combine like terms: 108 + 5.76 = 113.76 5.76 + 4.8x + x2 = 113.76 Factor a perfect square on the left side: (x + 2.4)(x + 2.4) = 113.76 Calculate the square root of the right side: 10.665833301 Break this problem into two subproblems by setting (x + 2.4) equal to 10.665833301 and -10.665833301.Subproblem 1
x + 2.4 = 10.665833301 Simplifying x + 2.4 = 10.665833301 Reorder the terms: 2.4 + x = 10.665833301 Solving 2.4 + x = 10.665833301 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.4' to each side of the equation. 2.4 + -2.4 + x = 10.665833301 + -2.4 Combine like terms: 2.4 + -2.4 = 0.0 0.0 + x = 10.665833301 + -2.4 x = 10.665833301 + -2.4 Combine like terms: 10.665833301 + -2.4 = 8.265833301 x = 8.265833301 Simplifying x = 8.265833301Subproblem 2
x + 2.4 = -10.665833301 Simplifying x + 2.4 = -10.665833301 Reorder the terms: 2.4 + x = -10.665833301 Solving 2.4 + x = -10.665833301 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.4' to each side of the equation. 2.4 + -2.4 + x = -10.665833301 + -2.4 Combine like terms: 2.4 + -2.4 = 0.0 0.0 + x = -10.665833301 + -2.4 x = -10.665833301 + -2.4 Combine like terms: -10.665833301 + -2.4 = -13.065833301 x = -13.065833301 Simplifying x = -13.065833301Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.265833301, -13.065833301}
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