(k+4)(k+7)=ksquared+28

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Solution for (k+4)(k+7)=ksquared+28 equation:


Simplifying
(k + 4)(k + 7) = ksquared + 28

Reorder the terms:
(4 + k)(k + 7) = ksquared + 28

Reorder the terms:
(4 + k)(7 + k) = ksquared + 28

Multiply (4 + k) * (7 + k)
(4(7 + k) + k(7 + k)) = ksquared + 28
((7 * 4 + k * 4) + k(7 + k)) = ksquared + 28
((28 + 4k) + k(7 + k)) = ksquared + 28
(28 + 4k + (7 * k + k * k)) = ksquared + 28
(28 + 4k + (7k + k2)) = ksquared + 28

Combine like terms: 4k + 7k = 11k
(28 + 11k + k2) = ksquared + 28

Reorder the terms:
28 + 11k + k2 = 28 + adekqrsu

Add '-28' to each side of the equation.
28 + 11k + -28 + k2 = 28 + -28 + adekqrsu

Reorder the terms:
28 + -28 + 11k + k2 = 28 + -28 + adekqrsu

Combine like terms: 28 + -28 = 0
0 + 11k + k2 = 28 + -28 + adekqrsu
11k + k2 = 28 + -28 + adekqrsu

Combine like terms: 28 + -28 = 0
11k + k2 = 0 + adekqrsu
11k + k2 = adekqrsu

Solving
11k + k2 = adekqrsu

Solving for variable 'k'.

Reorder the terms:
-1adekqrsu + 11k + k2 = adekqrsu + -1adekqrsu

Combine like terms: adekqrsu + -1adekqrsu = 0
-1adekqrsu + 11k + k2 = 0

Factor out the Greatest Common Factor (GCF), 'k'.
k(-1adeqrsu + 11 + k) = 0

Subproblem 1

Set the factor 'k' equal to zero and attempt to solve: Simplifying k = 0 Solving k = 0 Move all terms containing k to the left, all other terms to the right. Simplifying k = 0

Subproblem 2

Set the factor '(-1adeqrsu + 11 + k)' equal to zero and attempt to solve: Simplifying -1adeqrsu + 11 + k = 0 Reorder the terms: 11 + -1adeqrsu + k = 0 Solving 11 + -1adeqrsu + k = 0 Move all terms containing k to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -1adeqrsu + -11 + k = 0 + -11 Reorder the terms: 11 + -11 + -1adeqrsu + k = 0 + -11 Combine like terms: 11 + -11 = 0 0 + -1adeqrsu + k = 0 + -11 -1adeqrsu + k = 0 + -11 Combine like terms: 0 + -11 = -11 -1adeqrsu + k = -11 Add 'adeqrsu' to each side of the equation. -1adeqrsu + adeqrsu + k = -11 + adeqrsu Combine like terms: -1adeqrsu + adeqrsu = 0 0 + k = -11 + adeqrsu k = -11 + adeqrsu Simplifying k = -11 + adeqrsu

Solution

k = {0, -11 + adeqrsu}

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