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Simplifying -4k2 + 37k + -75 = -600k + 1800 Reorder the terms: -75 + 37k + -4k2 = -600k + 1800 Reorder the terms: -75 + 37k + -4k2 = 1800 + -600k Solving -75 + 37k + -4k2 = 1800 + -600k Solving for variable 'k'. Reorder the terms: -75 + -1800 + 37k + 600k + -4k2 = 1800 + -600k + -1800 + 600k Combine like terms: -75 + -1800 = -1875 -1875 + 37k + 600k + -4k2 = 1800 + -600k + -1800 + 600k Combine like terms: 37k + 600k = 637k -1875 + 637k + -4k2 = 1800 + -600k + -1800 + 600k Reorder the terms: -1875 + 637k + -4k2 = 1800 + -1800 + -600k + 600k Combine like terms: 1800 + -1800 = 0 -1875 + 637k + -4k2 = 0 + -600k + 600k -1875 + 637k + -4k2 = -600k + 600k Combine like terms: -600k + 600k = 0 -1875 + 637k + -4k2 = 0 Factor a trinomial. (-625 + 4k)(3 + -1k) = 0Subproblem 1
Set the factor '(-625 + 4k)' equal to zero and attempt to solve: Simplifying -625 + 4k = 0 Solving -625 + 4k = 0 Move all terms containing k to the left, all other terms to the right. Add '625' to each side of the equation. -625 + 625 + 4k = 0 + 625 Combine like terms: -625 + 625 = 0 0 + 4k = 0 + 625 4k = 0 + 625 Combine like terms: 0 + 625 = 625 4k = 625 Divide each side by '4'. k = 156.25 Simplifying k = 156.25Subproblem 2
Set the factor '(3 + -1k)' equal to zero and attempt to solve: Simplifying 3 + -1k = 0 Solving 3 + -1k = 0 Move all terms containing k to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1k = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1k = 0 + -3 -1k = 0 + -3 Combine like terms: 0 + -3 = -3 -1k = -3 Divide each side by '-1'. k = 3 Simplifying k = 3Solution
k = {156.25, 3}
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