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Simplifying 1000 = X2 + 45X + 450 Reorder the terms: 1000 = 450 + 45X + X2 Solving 1000 = 450 + 45X + X2 Solving for variable 'X'. Combine like terms: 1000 + -450 = 550 550 + -45X + -1X2 = 450 + 45X + X2 + -450 + -45X + -1X2 Reorder the terms: 550 + -45X + -1X2 = 450 + -450 + 45X + -45X + X2 + -1X2 Combine like terms: 450 + -450 = 0 550 + -45X + -1X2 = 0 + 45X + -45X + X2 + -1X2 550 + -45X + -1X2 = 45X + -45X + X2 + -1X2 Combine like terms: 45X + -45X = 0 550 + -45X + -1X2 = 0 + X2 + -1X2 550 + -45X + -1X2 = X2 + -1X2 Combine like terms: X2 + -1X2 = 0 550 + -45X + -1X2 = 0 Factor a trinomial. (10 + -1X)(55 + X) = 0Subproblem 1
Set the factor '(10 + -1X)' equal to zero and attempt to solve: Simplifying 10 + -1X = 0 Solving 10 + -1X = 0 Move all terms containing X to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + -1X = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -1X = 0 + -10 -1X = 0 + -10 Combine like terms: 0 + -10 = -10 -1X = -10 Divide each side by '-1'. X = 10 Simplifying X = 10Subproblem 2
Set the factor '(55 + X)' equal to zero and attempt to solve: Simplifying 55 + X = 0 Solving 55 + X = 0 Move all terms containing X to the left, all other terms to the right. Add '-55' to each side of the equation. 55 + -55 + X = 0 + -55 Combine like terms: 55 + -55 = 0 0 + X = 0 + -55 X = 0 + -55 Combine like terms: 0 + -55 = -55 X = -55 Simplifying X = -55Solution
X = {10, -55}
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