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Simplifying 0 = 1550 + 220x + -5x2 Solving 0 = 1550 + 220x + -5x2 Solving for variable 'x'. Combine like terms: 0 + -1550 = -1550 -1550 + -220x + 5x2 = 1550 + 220x + -5x2 + -1550 + -220x + 5x2 Reorder the terms: -1550 + -220x + 5x2 = 1550 + -1550 + 220x + -220x + -5x2 + 5x2 Combine like terms: 1550 + -1550 = 0 -1550 + -220x + 5x2 = 0 + 220x + -220x + -5x2 + 5x2 -1550 + -220x + 5x2 = 220x + -220x + -5x2 + 5x2 Combine like terms: 220x + -220x = 0 -1550 + -220x + 5x2 = 0 + -5x2 + 5x2 -1550 + -220x + 5x2 = -5x2 + 5x2 Combine like terms: -5x2 + 5x2 = 0 -1550 + -220x + 5x2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(-310 + -44x + x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-310 + -44x + x2)' equal to zero and attempt to solve: Simplifying -310 + -44x + x2 = 0 Solving -310 + -44x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '310' to each side of the equation. -310 + -44x + 310 + x2 = 0 + 310 Reorder the terms: -310 + 310 + -44x + x2 = 0 + 310 Combine like terms: -310 + 310 = 0 0 + -44x + x2 = 0 + 310 -44x + x2 = 0 + 310 Combine like terms: 0 + 310 = 310 -44x + x2 = 310 The x term is -44x. Take half its coefficient (-22). Square it (484) and add it to both sides. Add '484' to each side of the equation. -44x + 484 + x2 = 310 + 484 Reorder the terms: 484 + -44x + x2 = 310 + 484 Combine like terms: 310 + 484 = 794 484 + -44x + x2 = 794 Factor a perfect square on the left side: (x + -22)(x + -22) = 794 Calculate the square root of the right side: 28.178005607 Break this problem into two subproblems by setting (x + -22) equal to 28.178005607 and -28.178005607.Subproblem 1
x + -22 = 28.178005607 Simplifying x + -22 = 28.178005607 Reorder the terms: -22 + x = 28.178005607 Solving -22 + x = 28.178005607 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '22' to each side of the equation. -22 + 22 + x = 28.178005607 + 22 Combine like terms: -22 + 22 = 0 0 + x = 28.178005607 + 22 x = 28.178005607 + 22 Combine like terms: 28.178005607 + 22 = 50.178005607 x = 50.178005607 Simplifying x = 50.178005607Subproblem 2
x + -22 = -28.178005607 Simplifying x + -22 = -28.178005607 Reorder the terms: -22 + x = -28.178005607 Solving -22 + x = -28.178005607 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '22' to each side of the equation. -22 + 22 + x = -28.178005607 + 22 Combine like terms: -22 + 22 = 0 0 + x = -28.178005607 + 22 x = -28.178005607 + 22 Combine like terms: -28.178005607 + 22 = -6.178005607 x = -6.178005607 Simplifying x = -6.178005607Solution
The solution to the problem is based on the solutions from the subproblems. x = {50.178005607, -6.178005607}Solution
x = {50.178005607, -6.178005607}
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