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Simplifying 5x2 + 20x + -1200 = 0 Reorder the terms: -1200 + 20x + 5x2 = 0 Solving -1200 + 20x + 5x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '5'. 5(-240 + 4x + x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-240 + 4x + x2)' equal to zero and attempt to solve: Simplifying -240 + 4x + x2 = 0 Solving -240 + 4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '240' to each side of the equation. -240 + 4x + 240 + x2 = 0 + 240 Reorder the terms: -240 + 240 + 4x + x2 = 0 + 240 Combine like terms: -240 + 240 = 0 0 + 4x + x2 = 0 + 240 4x + x2 = 0 + 240 Combine like terms: 0 + 240 = 240 4x + x2 = 240 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 = 240 + 4 Reorder the terms: 4 + 4x + x2 = 240 + 4 Combine like terms: 240 + 4 = 244 4 + 4x + x2 = 244 Factor a perfect square on the left side: (x + 2)(x + 2) = 244 Calculate the square root of the right side: 15.620499352 Break this problem into two subproblems by setting (x + 2) equal to 15.620499352 and -15.620499352.Subproblem 1
x + 2 = 15.620499352 Simplifying x + 2 = 15.620499352 Reorder the terms: 2 + x = 15.620499352 Solving 2 + x = 15.620499352 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 = 15.620499352 + -2 Combine like terms: 2 + -2 = 0 0 + x = 15.620499352 + -2 x = 15.620499352 + -2 Combine like terms: 15.620499352 + -2 = 13.620499352 x = 13.620499352 Simplifying x = 13.620499352Subproblem 2
x + 2 = -15.620499352 Simplifying x + 2 = -15.620499352 Reorder the terms: 2 + x = -15.620499352 Solving 2 + x = -15.620499352 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 = -15.620499352 + -2 Combine like terms: 2 + -2 = 0 0 + x = -15.620499352 + -2 x = -15.620499352 + -2 Combine like terms: -15.620499352 + -2 = -17.620499352 x = -17.620499352 Simplifying x = -17.620499352Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.620499352, -17.620499352}Solution
x = {13.620499352, -17.620499352}
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