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Simplifying k^{2}+ 13k + 40 = 0 Reorder the terms: 40 + 13k + k^{2}= 0 Solving 40 + 13k + k^{2}= 0 Solving for variable 'k'. Factor a trinomial. (8 + k)(5 + k) = 0## Subproblem 1

Set the factor '(8 + k)' equal to zero and attempt to solve: Simplifying 8 + k = 0 Solving 8 + k = 0 Move all terms containing k to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + k = 0 + -8 Combine like terms: 8 + -8 = 0 0 + k = 0 + -8 k = 0 + -8 Combine like terms: 0 + -8 = -8 k = -8 Simplifying k = -8## Subproblem 2

Set the factor '(5 + k)' equal to zero and attempt to solve: Simplifying 5 + k = 0 Solving 5 + k = 0 Move all terms containing k to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + k = 0 + -5 Combine like terms: 5 + -5 = 0 0 + k = 0 + -5 k = 0 + -5 Combine like terms: 0 + -5 = -5 k = -5 Simplifying k = -5## Solution

k = {-8, -5}

| a^2+2a-24=0 | | n^2+15n+56=0 | | v^2+7v-8=0 | | b^2+9b+20=0 | | n^2-11n+24=0 | | x^2-13x+40=0 | | r^2-12r+35=0 | | m^2-5m=0 | | 5x^2=50 | | t^2+7t-35=2t-11 | | 2(x^2)-7x=1 | | x^2+4x-2m=0 | | 27x^2-5x=0 | | 7e^8+t=2 | | 13x^2-28x=0 | | 15n+3n^4-4n+12n^4+n= | | 2x^2-24x=-2x^2-7x-18 | | 30x^3-9x^2-3x=0 | | x^2+4=17 | | (x^3+2x+3x+6)= | | (2x^3+3)= | | (x^2+3)(x^3+2x^2+3x+6)+(2x^3+3)= | | 10y^2+33y+20=0 | | y^3+8y^2+16y=0 | | x^2+4x-60=0 | | 14x^2-5x=0 | | (x^3+y^5)(x^3-y^5)= | | 5x^2+11x+1=0 | | y^2-16y-4= | | y=5x^2-3x+5 | | 7x-28=2x^2-8x-3x+12 | | y=x^2+5x |

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