4x^2+17x-27=0

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Solution for 4x^2+17x-27=0 equation:


Simplifying
4x2 + 17x + -27 = 0

Reorder the terms:
-27 + 17x + 4x2 = 0

Solving
-27 + 17x + 4x2 = 0

Solving for variable 'x'.

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

Divide each side by '4'.
-6.75 + 4.25x + x2 = 0

Move the constant term to the right:

Add '6.75' to each side of the equation.
-6.75 + 4.25x + 6.75 + x2 = 0 + 6.75

Reorder the terms:
-6.75 + 6.75 + 4.25x + x2 = 0 + 6.75

Combine like terms: -6.75 + 6.75 = 0.00
0.00 + 4.25x + x2 = 0 + 6.75
4.25x + x2 = 0 + 6.75

Combine like terms: 0 + 6.75 = 6.75
4.25x + x2 = 6.75

The x term is 4.25x.  Take half its coefficient (2.125).
Square it (4.515625) and add it to both sides.

Add '4.515625' to each side of the equation.
4.25x + 4.515625 + x2 = 6.75 + 4.515625

Reorder the terms:
4.515625 + 4.25x + x2 = 6.75 + 4.515625

Combine like terms: 6.75 + 4.515625 = 11.265625
4.515625 + 4.25x + x2 = 11.265625

Factor a perfect square on the left side:
(x + 2.125)(x + 2.125) = 11.265625

Calculate the square root of the right side: 3.356430396

Break this problem into two subproblems by setting 
(x + 2.125) equal to 3.356430396 and -3.356430396.

Subproblem 1

x + 2.125 = 3.356430396 Simplifying x + 2.125 = 3.356430396 Reorder the terms: 2.125 + x = 3.356430396 Solving 2.125 + x = 3.356430396 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.125' to each side of the equation. 2.125 + -2.125 + x = 3.356430396 + -2.125 Combine like terms: 2.125 + -2.125 = 0.000 0.000 + x = 3.356430396 + -2.125 x = 3.356430396 + -2.125 Combine like terms: 3.356430396 + -2.125 = 1.231430396 x = 1.231430396 Simplifying x = 1.231430396

Subproblem 2

x + 2.125 = -3.356430396 Simplifying x + 2.125 = -3.356430396 Reorder the terms: 2.125 + x = -3.356430396 Solving 2.125 + x = -3.356430396 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.125' to each side of the equation. 2.125 + -2.125 + x = -3.356430396 + -2.125 Combine like terms: 2.125 + -2.125 = 0.000 0.000 + x = -3.356430396 + -2.125 x = -3.356430396 + -2.125 Combine like terms: -3.356430396 + -2.125 = -5.481430396 x = -5.481430396 Simplifying x = -5.481430396

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.231430396, -5.481430396}

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