0=5x^2+27x-35

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Solution for 0=5x^2+27x-35 equation:


Simplifying
0 = 5x2 + 27x + -35

Reorder the terms:
0 = -35 + 27x + 5x2

Solving
0 = -35 + 27x + 5x2

Solving for variable 'x'.

Combine like terms: 0 + 35 = 35
35 + -27x + -5x2 = -35 + 27x + 5x2 + 35 + -27x + -5x2

Reorder the terms:
35 + -27x + -5x2 = -35 + 35 + 27x + -27x + 5x2 + -5x2

Combine like terms: -35 + 35 = 0
35 + -27x + -5x2 = 0 + 27x + -27x + 5x2 + -5x2
35 + -27x + -5x2 = 27x + -27x + 5x2 + -5x2

Combine like terms: 27x + -27x = 0
35 + -27x + -5x2 = 0 + 5x2 + -5x2
35 + -27x + -5x2 = 5x2 + -5x2

Combine like terms: 5x2 + -5x2 = 0
35 + -27x + -5x2 = 0

Begin completing the square.  Divide all terms by
-5 the coefficient of the squared term: 

Divide each side by '-5'.
-7 + 5.4x + x2 = 0

Move the constant term to the right:

Add '7' to each side of the equation.
-7 + 5.4x + 7 + x2 = 0 + 7

Reorder the terms:
-7 + 7 + 5.4x + x2 = 0 + 7

Combine like terms: -7 + 7 = 0
0 + 5.4x + x2 = 0 + 7
5.4x + x2 = 0 + 7

Combine like terms: 0 + 7 = 7
5.4x + x2 = 7

The x term is 5.4x.  Take half its coefficient (2.7).
Square it (7.29) and add it to both sides.

Add '7.29' to each side of the equation.
5.4x + 7.29 + x2 = 7 + 7.29

Reorder the terms:
7.29 + 5.4x + x2 = 7 + 7.29

Combine like terms: 7 + 7.29 = 14.29
7.29 + 5.4x + x2 = 14.29

Factor a perfect square on the left side:
(x + 2.7)(x + 2.7) = 14.29

Calculate the square root of the right side: 3.780211634

Break this problem into two subproblems by setting 
(x + 2.7) equal to 3.780211634 and -3.780211634.

Subproblem 1

x + 2.7 = 3.780211634 Simplifying x + 2.7 = 3.780211634 Reorder the terms: 2.7 + x = 3.780211634 Solving 2.7 + x = 3.780211634 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.7' to each side of the equation. 2.7 + -2.7 + x = 3.780211634 + -2.7 Combine like terms: 2.7 + -2.7 = 0.0 0.0 + x = 3.780211634 + -2.7 x = 3.780211634 + -2.7 Combine like terms: 3.780211634 + -2.7 = 1.080211634 x = 1.080211634 Simplifying x = 1.080211634

Subproblem 2

x + 2.7 = -3.780211634 Simplifying x + 2.7 = -3.780211634 Reorder the terms: 2.7 + x = -3.780211634 Solving 2.7 + x = -3.780211634 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.7' to each side of the equation. 2.7 + -2.7 + x = -3.780211634 + -2.7 Combine like terms: 2.7 + -2.7 = 0.0 0.0 + x = -3.780211634 + -2.7 x = -3.780211634 + -2.7 Combine like terms: -3.780211634 + -2.7 = -6.480211634 x = -6.480211634 Simplifying x = -6.480211634

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.080211634, -6.480211634}

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