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Simplifying 4(x2 + 60x + -550) = 0 Reorder the terms: 4(-550 + 60x + x2) = 0 (-550 * 4 + 60x * 4 + x2 * 4) = 0 (-2200 + 240x + 4x2) = 0 Solving -2200 + 240x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(-550 + 60x + x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-550 + 60x + x2)' equal to zero and attempt to solve: Simplifying -550 + 60x + x2 = 0 Solving -550 + 60x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '550' to each side of the equation. -550 + 60x + 550 + x2 = 0 + 550 Reorder the terms: -550 + 550 + 60x + x2 = 0 + 550 Combine like terms: -550 + 550 = 0 0 + 60x + x2 = 0 + 550 60x + x2 = 0 + 550 Combine like terms: 0 + 550 = 550 60x + x2 = 550 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 = 550 + 900 Reorder the terms: 900 + 60x + x2 = 550 + 900 Combine like terms: 550 + 900 = 1450 900 + 60x + x2 = 1450 Factor a perfect square on the left side: (x + 30)(x + 30) = 1450 Calculate the square root of the right side: 38.078865529 Break this problem into two subproblems by setting (x + 30) equal to 38.078865529 and -38.078865529.Subproblem 1
x + 30 = 38.078865529 Simplifying x + 30 = 38.078865529 Reorder the terms: 30 + x = 38.078865529 Solving 30 + x = 38.078865529 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 = 38.078865529 + -30 Combine like terms: 30 + -30 = 0 0 + x = 38.078865529 + -30 x = 38.078865529 + -30 Combine like terms: 38.078865529 + -30 = 8.078865529 x = 8.078865529 Simplifying x = 8.078865529Subproblem 2
x + 30 = -38.078865529 Simplifying x + 30 = -38.078865529 Reorder the terms: 30 + x = -38.078865529 Solving 30 + x = -38.078865529 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 = -38.078865529 + -30 Combine like terms: 30 + -30 = 0 0 + x = -38.078865529 + -30 x = -38.078865529 + -30 Combine like terms: -38.078865529 + -30 = -68.078865529 x = -68.078865529 Simplifying x = -68.078865529Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.078865529, -68.078865529}Solution
x = {8.078865529, -68.078865529}
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