4k^2-16k-13=-7

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Solution for 4k^2-16k-13=-7 equation:


Simplifying
4k2 + -16k + -13 = -7

Reorder the terms:
-13 + -16k + 4k2 = -7

Solving
-13 + -16k + 4k2 = -7

Solving for variable 'k'.

Reorder the terms:
-13 + 7 + -16k + 4k2 = -7 + 7

Combine like terms: -13 + 7 = -6
-6 + -16k + 4k2 = -7 + 7

Combine like terms: -7 + 7 = 0
-6 + -16k + 4k2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-3 + -8k + 2k2) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(-3 + -8k + 2k2)' equal to zero and attempt to solve: Simplifying -3 + -8k + 2k2 = 0 Solving -3 + -8k + 2k2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -1.5 + -4k + k2 = 0 Move the constant term to the right: Add '1.5' to each side of the equation. -1.5 + -4k + 1.5 + k2 = 0 + 1.5 Reorder the terms: -1.5 + 1.5 + -4k + k2 = 0 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + -4k + k2 = 0 + 1.5 -4k + k2 = 0 + 1.5 Combine like terms: 0 + 1.5 = 1.5 -4k + k2 = 1.5 The k term is -4k. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4k + 4 + k2 = 1.5 + 4 Reorder the terms: 4 + -4k + k2 = 1.5 + 4 Combine like terms: 1.5 + 4 = 5.5 4 + -4k + k2 = 5.5 Factor a perfect square on the left side: (k + -2)(k + -2) = 5.5 Calculate the square root of the right side: 2.34520788 Break this problem into two subproblems by setting (k + -2) equal to 2.34520788 and -2.34520788.

Subproblem 1

k + -2 = 2.34520788 Simplifying k + -2 = 2.34520788 Reorder the terms: -2 + k = 2.34520788 Solving -2 + k = 2.34520788 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + k = 2.34520788 + 2 Combine like terms: -2 + 2 = 0 0 + k = 2.34520788 + 2 k = 2.34520788 + 2 Combine like terms: 2.34520788 + 2 = 4.34520788 k = 4.34520788 Simplifying k = 4.34520788

Subproblem 2

k + -2 = -2.34520788 Simplifying k + -2 = -2.34520788 Reorder the terms: -2 + k = -2.34520788 Solving -2 + k = -2.34520788 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + k = -2.34520788 + 2 Combine like terms: -2 + 2 = 0 0 + k = -2.34520788 + 2 k = -2.34520788 + 2 Combine like terms: -2.34520788 + 2 = -0.34520788 k = -0.34520788 Simplifying k = -0.34520788

Solution

The solution to the problem is based on the solutions from the subproblems. k = {4.34520788, -0.34520788}

Solution

k = {4.34520788, -0.34520788}

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