(4k-3)(4k-3)=50

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Solution for (4k-3)(4k-3)=50 equation:


Simplifying
(4k + -3)(4k + -3) = 50

Reorder the terms:
(-3 + 4k)(4k + -3) = 50

Reorder the terms:
(-3 + 4k)(-3 + 4k) = 50

Multiply (-3 + 4k) * (-3 + 4k)
(-3(-3 + 4k) + 4k * (-3 + 4k)) = 50
((-3 * -3 + 4k * -3) + 4k * (-3 + 4k)) = 50
((9 + -12k) + 4k * (-3 + 4k)) = 50
(9 + -12k + (-3 * 4k + 4k * 4k)) = 50
(9 + -12k + (-12k + 16k2)) = 50

Combine like terms: -12k + -12k = -24k
(9 + -24k + 16k2) = 50

Solving
9 + -24k + 16k2 = 50

Solving for variable 'k'.

Reorder the terms:
9 + -50 + -24k + 16k2 = 50 + -50

Combine like terms: 9 + -50 = -41
-41 + -24k + 16k2 = 50 + -50

Combine like terms: 50 + -50 = 0
-41 + -24k + 16k2 = 0

Begin completing the square.  Divide all terms by
16 the coefficient of the squared term: 

Divide each side by '16'.
-2.5625 + -1.5k + k2 = 0

Move the constant term to the right:

Add '2.5625' to each side of the equation.
-2.5625 + -1.5k + 2.5625 + k2 = 0 + 2.5625

Reorder the terms:
-2.5625 + 2.5625 + -1.5k + k2 = 0 + 2.5625

Combine like terms: -2.5625 + 2.5625 = 0.0000
0.0000 + -1.5k + k2 = 0 + 2.5625
-1.5k + k2 = 0 + 2.5625

Combine like terms: 0 + 2.5625 = 2.5625
-1.5k + k2 = 2.5625

The k term is -1.5k.  Take half its coefficient (-0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
-1.5k + 0.5625 + k2 = 2.5625 + 0.5625

Reorder the terms:
0.5625 + -1.5k + k2 = 2.5625 + 0.5625

Combine like terms: 2.5625 + 0.5625 = 3.125
0.5625 + -1.5k + k2 = 3.125

Factor a perfect square on the left side:
(k + -0.75)(k + -0.75) = 3.125

Calculate the square root of the right side: 1.767766953

Break this problem into two subproblems by setting 
(k + -0.75) equal to 1.767766953 and -1.767766953.

Subproblem 1

k + -0.75 = 1.767766953 Simplifying k + -0.75 = 1.767766953 Reorder the terms: -0.75 + k = 1.767766953 Solving -0.75 + k = 1.767766953 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + k = 1.767766953 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + k = 1.767766953 + 0.75 k = 1.767766953 + 0.75 Combine like terms: 1.767766953 + 0.75 = 2.517766953 k = 2.517766953 Simplifying k = 2.517766953

Subproblem 2

k + -0.75 = -1.767766953 Simplifying k + -0.75 = -1.767766953 Reorder the terms: -0.75 + k = -1.767766953 Solving -0.75 + k = -1.767766953 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + k = -1.767766953 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + k = -1.767766953 + 0.75 k = -1.767766953 + 0.75 Combine like terms: -1.767766953 + 0.75 = -1.017766953 k = -1.017766953 Simplifying k = -1.017766953

Solution

The solution to the problem is based on the solutions from the subproblems. k = {2.517766953, -1.017766953}

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