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Simplifying 2x2 + -20x + -3600 = 0 Reorder the terms: -3600 + -20x + 2x2 = 0 Solving -3600 + -20x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-1800 + -10x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-1800 + -10x + x2)' equal to zero and attempt to solve: Simplifying -1800 + -10x + x2 = 0 Solving -1800 + -10x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '1800' to each side of the equation. -1800 + -10x + 1800 + x2 = 0 + 1800 Reorder the terms: -1800 + 1800 + -10x + x2 = 0 + 1800 Combine like terms: -1800 + 1800 = 0 0 + -10x + x2 = 0 + 1800 -10x + x2 = 0 + 1800 Combine like terms: 0 + 1800 = 1800 -10x + x2 = 1800 The x term is -10x. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10x + 25 + x2 = 1800 + 25 Reorder the terms: 25 + -10x + x2 = 1800 + 25 Combine like terms: 1800 + 25 = 1825 25 + -10x + x2 = 1825 Factor a perfect square on the left side: (x + -5)(x + -5) = 1825 Calculate the square root of the right side: 42.720018727 Break this problem into two subproblems by setting (x + -5) equal to 42.720018727 and -42.720018727.Subproblem 1
x + -5 = 42.720018727 Simplifying x + -5 = 42.720018727 Reorder the terms: -5 + x = 42.720018727 Solving -5 + x = 42.720018727 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = 42.720018727 + 5 Combine like terms: -5 + 5 = 0 0 + x = 42.720018727 + 5 x = 42.720018727 + 5 Combine like terms: 42.720018727 + 5 = 47.720018727 x = 47.720018727 Simplifying x = 47.720018727Subproblem 2
x + -5 = -42.720018727 Simplifying x + -5 = -42.720018727 Reorder the terms: -5 + x = -42.720018727 Solving -5 + x = -42.720018727 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = -42.720018727 + 5 Combine like terms: -5 + 5 = 0 0 + x = -42.720018727 + 5 x = -42.720018727 + 5 Combine like terms: -42.720018727 + 5 = -37.720018727 x = -37.720018727 Simplifying x = -37.720018727Solution
The solution to the problem is based on the solutions from the subproblems. x = {47.720018727, -37.720018727}Solution
x = {47.720018727, -37.720018727}
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