4k^2+26k-36=0

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Solution for 4k^2+26k-36=0 equation:


Simplifying
4k2 + 26k + -36 = 0

Reorder the terms:
-36 + 26k + 4k2 = 0

Solving
-36 + 26k + 4k2 = 0

Solving for variable 'k'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-18 + 13k + 2k2) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(-18 + 13k + 2k2)' equal to zero and attempt to solve: Simplifying -18 + 13k + 2k2 = 0 Solving -18 + 13k + 2k2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -9 + 6.5k + k2 = 0 Move the constant term to the right: Add '9' to each side of the equation. -9 + 6.5k + 9 + k2 = 0 + 9 Reorder the terms: -9 + 9 + 6.5k + k2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + 6.5k + k2 = 0 + 9 6.5k + k2 = 0 + 9 Combine like terms: 0 + 9 = 9 6.5k + k2 = 9 The k term is 6.5k. Take half its coefficient (3.25). Square it (10.5625) and add it to both sides. Add '10.5625' to each side of the equation. 6.5k + 10.5625 + k2 = 9 + 10.5625 Reorder the terms: 10.5625 + 6.5k + k2 = 9 + 10.5625 Combine like terms: 9 + 10.5625 = 19.5625 10.5625 + 6.5k + k2 = 19.5625 Factor a perfect square on the left side: (k + 3.25)(k + 3.25) = 19.5625 Calculate the square root of the right side: 4.422951503 Break this problem into two subproblems by setting (k + 3.25) equal to 4.422951503 and -4.422951503.

Subproblem 1

k + 3.25 = 4.422951503 Simplifying k + 3.25 = 4.422951503 Reorder the terms: 3.25 + k = 4.422951503 Solving 3.25 + k = 4.422951503 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-3.25' to each side of the equation. 3.25 + -3.25 + k = 4.422951503 + -3.25 Combine like terms: 3.25 + -3.25 = 0.00 0.00 + k = 4.422951503 + -3.25 k = 4.422951503 + -3.25 Combine like terms: 4.422951503 + -3.25 = 1.172951503 k = 1.172951503 Simplifying k = 1.172951503

Subproblem 2

k + 3.25 = -4.422951503 Simplifying k + 3.25 = -4.422951503 Reorder the terms: 3.25 + k = -4.422951503 Solving 3.25 + k = -4.422951503 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-3.25' to each side of the equation. 3.25 + -3.25 + k = -4.422951503 + -3.25 Combine like terms: 3.25 + -3.25 = 0.00 0.00 + k = -4.422951503 + -3.25 k = -4.422951503 + -3.25 Combine like terms: -4.422951503 + -3.25 = -7.672951503 k = -7.672951503 Simplifying k = -7.672951503

Solution

The solution to the problem is based on the solutions from the subproblems. k = {1.172951503, -7.672951503}

Solution

k = {1.172951503, -7.672951503}

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