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Simplifying 4x2 + 280x + -4800 = 0 Reorder the terms: -4800 + 280x + 4x2 = 0 Solving -4800 + 280x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(-1200 + 70x + x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-1200 + 70x + x2)' equal to zero and attempt to solve: Simplifying -1200 + 70x + x2 = 0 Solving -1200 + 70x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '1200' to each side of the equation. -1200 + 70x + 1200 + x2 = 0 + 1200 Reorder the terms: -1200 + 1200 + 70x + x2 = 0 + 1200 Combine like terms: -1200 + 1200 = 0 0 + 70x + x2 = 0 + 1200 70x + x2 = 0 + 1200 Combine like terms: 0 + 1200 = 1200 70x + x2 = 1200 The x term is 70x. Take half its coefficient (35). Square it (1225) and add it to both sides. Add '1225' to each side of the equation. 70x + 1225 + x2 = 1200 + 1225 Reorder the terms: 1225 + 70x + x2 = 1200 + 1225 Combine like terms: 1200 + 1225 = 2425 1225 + 70x + x2 = 2425 Factor a perfect square on the left side: (x + 35)(x + 35) = 2425 Calculate the square root of the right side: 49.244289009 Break this problem into two subproblems by setting (x + 35) equal to 49.244289009 and -49.244289009.Subproblem 1
x + 35 = 49.244289009 Simplifying x + 35 = 49.244289009 Reorder the terms: 35 + x = 49.244289009 Solving 35 + x = 49.244289009 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-35' to each side of the equation. 35 + -35 + x = 49.244289009 + -35 Combine like terms: 35 + -35 = 0 0 + x = 49.244289009 + -35 x = 49.244289009 + -35 Combine like terms: 49.244289009 + -35 = 14.244289009 x = 14.244289009 Simplifying x = 14.244289009Subproblem 2
x + 35 = -49.244289009 Simplifying x + 35 = -49.244289009 Reorder the terms: 35 + x = -49.244289009 Solving 35 + x = -49.244289009 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-35' to each side of the equation. 35 + -35 + x = -49.244289009 + -35 Combine like terms: 35 + -35 = 0 0 + x = -49.244289009 + -35 x = -49.244289009 + -35 Combine like terms: -49.244289009 + -35 = -84.244289009 x = -84.244289009 Simplifying x = -84.244289009Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.244289009, -84.244289009}Solution
x = {14.244289009, -84.244289009}
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