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Simplifying 2(x2 + 60x + -200) = 0 Reorder the terms: 2(-200 + 60x + x2) = 0 (-200 * 2 + 60x * 2 + x2 * 2) = 0 (-400 + 120x + 2x2) = 0 Solving -400 + 120x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-200 + 60x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-200 + 60x + x2)' equal to zero and attempt to solve: Simplifying -200 + 60x + x2 = 0 Solving -200 + 60x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '200' to each side of the equation. -200 + 60x + 200 + x2 = 0 + 200 Reorder the terms: -200 + 200 + 60x + x2 = 0 + 200 Combine like terms: -200 + 200 = 0 0 + 60x + x2 = 0 + 200 60x + x2 = 0 + 200 Combine like terms: 0 + 200 = 200 60x + x2 = 200 The x term is 60x. Take half its coefficient (30). Square it (900) and add it to both sides. Add '900' to each side of the equation. 60x + 900 + x2 = 200 + 900 Reorder the terms: 900 + 60x + x2 = 200 + 900 Combine like terms: 200 + 900 = 1100 900 + 60x + x2 = 1100 Factor a perfect square on the left side: (x + 30)(x + 30) = 1100 Calculate the square root of the right side: 33.166247904 Break this problem into two subproblems by setting (x + 30) equal to 33.166247904 and -33.166247904.Subproblem 1
x + 30 = 33.166247904 Simplifying x + 30 = 33.166247904 Reorder the terms: 30 + x = 33.166247904 Solving 30 + x = 33.166247904 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-30' to each side of the equation. 30 + -30 + x = 33.166247904 + -30 Combine like terms: 30 + -30 = 0 0 + x = 33.166247904 + -30 x = 33.166247904 + -30 Combine like terms: 33.166247904 + -30 = 3.166247904 x = 3.166247904 Simplifying x = 3.166247904Subproblem 2
x + 30 = -33.166247904 Simplifying x + 30 = -33.166247904 Reorder the terms: 30 + x = -33.166247904 Solving 30 + x = -33.166247904 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-30' to each side of the equation. 30 + -30 + x = -33.166247904 + -30 Combine like terms: 30 + -30 = 0 0 + x = -33.166247904 + -30 x = -33.166247904 + -30 Combine like terms: -33.166247904 + -30 = -63.166247904 x = -63.166247904 Simplifying x = -63.166247904Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.166247904, -63.166247904}Solution
x = {3.166247904, -63.166247904}
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