5x^2+21x-42=0

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Solution for 5x^2+21x-42=0 equation:


Simplifying
5x2 + 21x + -42 = 0

Reorder the terms:
-42 + 21x + 5x2 = 0

Solving
-42 + 21x + 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'.
-8.4 + 4.2x + x2 = 0

Move the constant term to the right:

Add '8.4' to each side of the equation.
-8.4 + 4.2x + 8.4 + x2 = 0 + 8.4

Reorder the terms:
-8.4 + 8.4 + 4.2x + x2 = 0 + 8.4

Combine like terms: -8.4 + 8.4 = 0.0
0.0 + 4.2x + x2 = 0 + 8.4
4.2x + x2 = 0 + 8.4

Combine like terms: 0 + 8.4 = 8.4
4.2x + x2 = 8.4

The x term is 4.2x.  Take half its coefficient (2.1).
Square it (4.41) and add it to both sides.

Add '4.41' to each side of the equation.
4.2x + 4.41 + x2 = 8.4 + 4.41

Reorder the terms:
4.41 + 4.2x + x2 = 8.4 + 4.41

Combine like terms: 8.4 + 4.41 = 12.81
4.41 + 4.2x + x2 = 12.81

Factor a perfect square on the left side:
(x + 2.1)(x + 2.1) = 12.81

Calculate the square root of the right side: 3.579106034

Break this problem into two subproblems by setting 
(x + 2.1) equal to 3.579106034 and -3.579106034.

Subproblem 1

x + 2.1 = 3.579106034 Simplifying x + 2.1 = 3.579106034 Reorder the terms: 2.1 + x = 3.579106034 Solving 2.1 + x = 3.579106034 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.1' to each side of the equation. 2.1 + -2.1 + x = 3.579106034 + -2.1 Combine like terms: 2.1 + -2.1 = 0.0 0.0 + x = 3.579106034 + -2.1 x = 3.579106034 + -2.1 Combine like terms: 3.579106034 + -2.1 = 1.479106034 x = 1.479106034 Simplifying x = 1.479106034

Subproblem 2

x + 2.1 = -3.579106034 Simplifying x + 2.1 = -3.579106034 Reorder the terms: 2.1 + x = -3.579106034 Solving 2.1 + x = -3.579106034 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.1' to each side of the equation. 2.1 + -2.1 + x = -3.579106034 + -2.1 Combine like terms: 2.1 + -2.1 = 0.0 0.0 + x = -3.579106034 + -2.1 x = -3.579106034 + -2.1 Combine like terms: -3.579106034 + -2.1 = -5.679106034 x = -5.679106034 Simplifying x = -5.679106034

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.479106034, -5.679106034}

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