x^2+21x-12=0

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Solution for x^2+21x-12=0 equation:


Simplifying
x2 + 21x + -12 = 0

Reorder the terms:
-12 + 21x + x2 = 0

Solving
-12 + 21x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '12' to each side of the equation.
-12 + 21x + 12 + x2 = 0 + 12

Reorder the terms:
-12 + 12 + 21x + x2 = 0 + 12

Combine like terms: -12 + 12 = 0
0 + 21x + x2 = 0 + 12
21x + x2 = 0 + 12

Combine like terms: 0 + 12 = 12
21x + x2 = 12

The x term is 21x.  Take half its coefficient (10.5).
Square it (110.25) and add it to both sides.

Add '110.25' to each side of the equation.
21x + 110.25 + x2 = 12 + 110.25

Reorder the terms:
110.25 + 21x + x2 = 12 + 110.25

Combine like terms: 12 + 110.25 = 122.25
110.25 + 21x + x2 = 122.25

Factor a perfect square on the left side:
(x + 10.5)(x + 10.5) = 122.25

Calculate the square root of the right side: 11.056672194

Break this problem into two subproblems by setting 
(x + 10.5) equal to 11.056672194 and -11.056672194.

Subproblem 1

x + 10.5 = 11.056672194 Simplifying x + 10.5 = 11.056672194 Reorder the terms: 10.5 + x = 11.056672194 Solving 10.5 + x = 11.056672194 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10.5' to each side of the equation. 10.5 + -10.5 + x = 11.056672194 + -10.5 Combine like terms: 10.5 + -10.5 = 0.0 0.0 + x = 11.056672194 + -10.5 x = 11.056672194 + -10.5 Combine like terms: 11.056672194 + -10.5 = 0.556672194 x = 0.556672194 Simplifying x = 0.556672194

Subproblem 2

x + 10.5 = -11.056672194 Simplifying x + 10.5 = -11.056672194 Reorder the terms: 10.5 + x = -11.056672194 Solving 10.5 + x = -11.056672194 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10.5' to each side of the equation. 10.5 + -10.5 + x = -11.056672194 + -10.5 Combine like terms: 10.5 + -10.5 = 0.0 0.0 + x = -11.056672194 + -10.5 x = -11.056672194 + -10.5 Combine like terms: -11.056672194 + -10.5 = -21.556672194 x = -21.556672194 Simplifying x = -21.556672194

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.556672194, -21.556672194}

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