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Simplifying 5x2 + 40x + -2700 = 0 Reorder the terms: -2700 + 40x + 5x2 = 0 Solving -2700 + 40x + 5x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '5'. 5(-540 + 8x + x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-540 + 8x + x2)' equal to zero and attempt to solve: Simplifying -540 + 8x + x2 = 0 Solving -540 + 8x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '540' to each side of the equation. -540 + 8x + 540 + x2 = 0 + 540 Reorder the terms: -540 + 540 + 8x + x2 = 0 + 540 Combine like terms: -540 + 540 = 0 0 + 8x + x2 = 0 + 540 8x + x2 = 0 + 540 Combine like terms: 0 + 540 = 540 8x + x2 = 540 The x term is 8x. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8x + 16 + x2 = 540 + 16 Reorder the terms: 16 + 8x + x2 = 540 + 16 Combine like terms: 540 + 16 = 556 16 + 8x + x2 = 556 Factor a perfect square on the left side: (x + 4)(x + 4) = 556 Calculate the square root of the right side: 23.579652245 Break this problem into two subproblems by setting (x + 4) equal to 23.579652245 and -23.579652245.Subproblem 1
x + 4 = 23.579652245 Simplifying x + 4 = 23.579652245 Reorder the terms: 4 + x = 23.579652245 Solving 4 + x = 23.579652245 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 23.579652245 + -4 Combine like terms: 4 + -4 = 0 0 + x = 23.579652245 + -4 x = 23.579652245 + -4 Combine like terms: 23.579652245 + -4 = 19.579652245 x = 19.579652245 Simplifying x = 19.579652245Subproblem 2
x + 4 = -23.579652245 Simplifying x + 4 = -23.579652245 Reorder the terms: 4 + x = -23.579652245 Solving 4 + x = -23.579652245 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = -23.579652245 + -4 Combine like terms: 4 + -4 = 0 0 + x = -23.579652245 + -4 x = -23.579652245 + -4 Combine like terms: -23.579652245 + -4 = -27.579652245 x = -27.579652245 Simplifying x = -27.579652245Solution
The solution to the problem is based on the solutions from the subproblems. x = {19.579652245, -27.579652245}Solution
x = {19.579652245, -27.579652245}
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