5x^2+36x-21=0

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Solution for 5x^2+36x-21=0 equation:


Simplifying
5x2 + 36x + -21 = 0

Reorder the terms:
-21 + 36x + 5x2 = 0

Solving
-21 + 36x + 5x2 = 0

Solving for variable 'x'.

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

Divide each side by '5'.
-4.2 + 7.2x + x2 = 0

Move the constant term to the right:

Add '4.2' to each side of the equation.
-4.2 + 7.2x + 4.2 + x2 = 0 + 4.2

Reorder the terms:
-4.2 + 4.2 + 7.2x + x2 = 0 + 4.2

Combine like terms: -4.2 + 4.2 = 0.0
0.0 + 7.2x + x2 = 0 + 4.2
7.2x + x2 = 0 + 4.2

Combine like terms: 0 + 4.2 = 4.2
7.2x + x2 = 4.2

The x term is 7.2x.  Take half its coefficient (3.6).
Square it (12.96) and add it to both sides.

Add '12.96' to each side of the equation.
7.2x + 12.96 + x2 = 4.2 + 12.96

Reorder the terms:
12.96 + 7.2x + x2 = 4.2 + 12.96

Combine like terms: 4.2 + 12.96 = 17.16
12.96 + 7.2x + x2 = 17.16

Factor a perfect square on the left side:
(x + 3.6)(x + 3.6) = 17.16

Calculate the square root of the right side: 4.142463035

Break this problem into two subproblems by setting 
(x + 3.6) equal to 4.142463035 and -4.142463035.

Subproblem 1

x + 3.6 = 4.142463035 Simplifying x + 3.6 = 4.142463035 Reorder the terms: 3.6 + x = 4.142463035 Solving 3.6 + x = 4.142463035 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.6' to each side of the equation. 3.6 + -3.6 + x = 4.142463035 + -3.6 Combine like terms: 3.6 + -3.6 = 0.0 0.0 + x = 4.142463035 + -3.6 x = 4.142463035 + -3.6 Combine like terms: 4.142463035 + -3.6 = 0.542463035 x = 0.542463035 Simplifying x = 0.542463035

Subproblem 2

x + 3.6 = -4.142463035 Simplifying x + 3.6 = -4.142463035 Reorder the terms: 3.6 + x = -4.142463035 Solving 3.6 + x = -4.142463035 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.6' to each side of the equation. 3.6 + -3.6 + x = -4.142463035 + -3.6 Combine like terms: 3.6 + -3.6 = 0.0 0.0 + x = -4.142463035 + -3.6 x = -4.142463035 + -3.6 Combine like terms: -4.142463035 + -3.6 = -7.742463035 x = -7.742463035 Simplifying x = -7.742463035

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.542463035, -7.742463035}

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