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Simplifying -100x2 + 1200x + 4400 = 0 Reorder the terms: 4400 + 1200x + -100x2 = 0 Solving 4400 + 1200x + -100x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '100'. 100(44 + 12x + -1x2) = 0 Ignore the factor 100.Subproblem 1
Set the factor '(44 + 12x + -1x2)' equal to zero and attempt to solve: Simplifying 44 + 12x + -1x2 = 0 Solving 44 + 12x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -44 + -12x + x2 = 0 Move the constant term to the right: Add '44' to each side of the equation. -44 + -12x + 44 + x2 = 0 + 44 Reorder the terms: -44 + 44 + -12x + x2 = 0 + 44 Combine like terms: -44 + 44 = 0 0 + -12x + x2 = 0 + 44 -12x + x2 = 0 + 44 Combine like terms: 0 + 44 = 44 -12x + x2 = 44 The x term is -12x. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12x + 36 + x2 = 44 + 36 Reorder the terms: 36 + -12x + x2 = 44 + 36 Combine like terms: 44 + 36 = 80 36 + -12x + x2 = 80 Factor a perfect square on the left side: (x + -6)(x + -6) = 80 Calculate the square root of the right side: 8.94427191 Break this problem into two subproblems by setting (x + -6) equal to 8.94427191 and -8.94427191.Subproblem 1
x + -6 = 8.94427191 Simplifying x + -6 = 8.94427191 Reorder the terms: -6 + x = 8.94427191 Solving -6 + x = 8.94427191 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = 8.94427191 + 6 Combine like terms: -6 + 6 = 0 0 + x = 8.94427191 + 6 x = 8.94427191 + 6 Combine like terms: 8.94427191 + 6 = 14.94427191 x = 14.94427191 Simplifying x = 14.94427191Subproblem 2
x + -6 = -8.94427191 Simplifying x + -6 = -8.94427191 Reorder the terms: -6 + x = -8.94427191 Solving -6 + x = -8.94427191 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = -8.94427191 + 6 Combine like terms: -6 + 6 = 0 0 + x = -8.94427191 + 6 x = -8.94427191 + 6 Combine like terms: -8.94427191 + 6 = -2.94427191 x = -2.94427191 Simplifying x = -2.94427191Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.94427191, -2.94427191}Solution
x = {14.94427191, -2.94427191}
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