27x+100=4x^2

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Solution for 27x+100=4x^2 equation:


Simplifying
27x + 100 = 4x2

Reorder the terms:
100 + 27x = 4x2

Solving
100 + 27x = 4x2

Solving for variable 'x'.

Combine like terms: 4x2 + -4x2 = 0
100 + 27x + -4x2 = 0

Begin completing the square.  Divide all terms by
-4 the coefficient of the squared term: 

Divide each side by '-4'.
-25 + -6.75x + x2 = 0

Move the constant term to the right:

Add '25' to each side of the equation.
-25 + -6.75x + 25 + x2 = 0 + 25

Reorder the terms:
-25 + 25 + -6.75x + x2 = 0 + 25

Combine like terms: -25 + 25 = 0
0 + -6.75x + x2 = 0 + 25
-6.75x + x2 = 0 + 25

Combine like terms: 0 + 25 = 25
-6.75x + x2 = 25

The x term is -6.75x.  Take half its coefficient (-3.375).
Square it (11.390625) and add it to both sides.

Add '11.390625' to each side of the equation.
-6.75x + 11.390625 + x2 = 25 + 11.390625

Reorder the terms:
11.390625 + -6.75x + x2 = 25 + 11.390625

Combine like terms: 25 + 11.390625 = 36.390625
11.390625 + -6.75x + x2 = 36.390625

Factor a perfect square on the left side:
(x + -3.375)(x + -3.375) = 36.390625

Calculate the square root of the right side: 6.032464256

Break this problem into two subproblems by setting 
(x + -3.375) equal to 6.032464256 and -6.032464256.

Subproblem 1

x + -3.375 = 6.032464256 Simplifying x + -3.375 = 6.032464256 Reorder the terms: -3.375 + x = 6.032464256 Solving -3.375 + x = 6.032464256 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.375' to each side of the equation. -3.375 + 3.375 + x = 6.032464256 + 3.375 Combine like terms: -3.375 + 3.375 = 0.000 0.000 + x = 6.032464256 + 3.375 x = 6.032464256 + 3.375 Combine like terms: 6.032464256 + 3.375 = 9.407464256 x = 9.407464256 Simplifying x = 9.407464256

Subproblem 2

x + -3.375 = -6.032464256 Simplifying x + -3.375 = -6.032464256 Reorder the terms: -3.375 + x = -6.032464256 Solving -3.375 + x = -6.032464256 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.375' to each side of the equation. -3.375 + 3.375 + x = -6.032464256 + 3.375 Combine like terms: -3.375 + 3.375 = 0.000 0.000 + x = -6.032464256 + 3.375 x = -6.032464256 + 3.375 Combine like terms: -6.032464256 + 3.375 = -2.657464256 x = -2.657464256 Simplifying x = -2.657464256

Solution

The solution to the problem is based on the solutions from the subproblems. x = {9.407464256, -2.657464256}

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