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Simplifying 4(x2 + 60x + -1020) = 0 Reorder the terms: 4(-1020 + 60x + x2) = 0 (-1020 * 4 + 60x * 4 + x2 * 4) = 0 (-4080 + 240x + 4x2) = 0 Solving -4080 + 240x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(-1020 + 60x + x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-1020 + 60x + x2)' equal to zero and attempt to solve: Simplifying -1020 + 60x + x2 = 0 Solving -1020 + 60x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '1020' to each side of the equation. -1020 + 60x + 1020 + x2 = 0 + 1020 Reorder the terms: -1020 + 1020 + 60x + x2 = 0 + 1020 Combine like terms: -1020 + 1020 = 0 0 + 60x + x2 = 0 + 1020 60x + x2 = 0 + 1020 Combine like terms: 0 + 1020 = 1020 60x + x2 = 1020 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 = 1020 + 900 Reorder the terms: 900 + 60x + x2 = 1020 + 900 Combine like terms: 1020 + 900 = 1920 900 + 60x + x2 = 1920 Factor a perfect square on the left side: (x + 30)(x + 30) = 1920 Calculate the square root of the right side: 43.8178046 Break this problem into two subproblems by setting (x + 30) equal to 43.8178046 and -43.8178046.Subproblem 1
x + 30 = 43.8178046 Simplifying x + 30 = 43.8178046 Reorder the terms: 30 + x = 43.8178046 Solving 30 + x = 43.8178046 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 = 43.8178046 + -30 Combine like terms: 30 + -30 = 0 0 + x = 43.8178046 + -30 x = 43.8178046 + -30 Combine like terms: 43.8178046 + -30 = 13.8178046 x = 13.8178046 Simplifying x = 13.8178046Subproblem 2
x + 30 = -43.8178046 Simplifying x + 30 = -43.8178046 Reorder the terms: 30 + x = -43.8178046 Solving 30 + x = -43.8178046 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 = -43.8178046 + -30 Combine like terms: 30 + -30 = 0 0 + x = -43.8178046 + -30 x = -43.8178046 + -30 Combine like terms: -43.8178046 + -30 = -73.8178046 x = -73.8178046 Simplifying x = -73.8178046Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.8178046, -73.8178046}Solution
x = {13.8178046, -73.8178046}
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