-3x^2+28x-21=

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Solution for -3x^2+28x-21= equation: 


Simplifying
-3x2 + 28x + -21 = 0

Reorder the terms:
-21 + 28x + -3x2 = 0

Solving
-21 + 28x + -3x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-3 the coefficient of the squared term: 

Divide each side by '-3'.
7 + -9.333333333x + x2 = 0

Move the constant term to the right:

Add '-7' to each side of the equation.
7 + -9.333333333x + -7 + x2 = 0 + -7

Reorder the terms:
7 + -7 + -9.333333333x + x2 = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -9.333333333x + x2 = 0 + -7
-9.333333333x + x2 = 0 + -7

Combine like terms: 0 + -7 = -7
-9.333333333x + x2 = -7

The x term is -9.333333333x.  Take half its coefficient (-4.666666667).
Square it (21.77777778) and add it to both sides.

Add '21.77777778' to each side of the equation.
-9.333333333x + 21.77777778 + x2 = -7 + 21.77777778

Reorder the terms:
21.77777778 + -9.333333333x + x2 = -7 + 21.77777778

Combine like terms: -7 + 21.77777778 = 14.77777778
21.77777778 + -9.333333333x + x2 = 14.77777778

Factor a perfect square on the left side:
(x + -4.666666667)(x + -4.666666667) = 14.77777778

Calculate the square root of the right side: 3.844187532

Break this problem into two subproblems by setting 
(x + -4.666666667) equal to 3.844187532 and -3.844187532.


Subproblem 1
x + -4.666666667 = 3.844187532

Simplifying
x + -4.666666667 = 3.844187532

Reorder the terms:
-4.666666667 + x = 3.844187532

Solving
-4.666666667 + x = 3.844187532

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '4.666666667' to each side of the equation.
-4.666666667 + 4.666666667 + x = 3.844187532 + 4.666666667

Combine like terms: -4.666666667 + 4.666666667 = 0.000000000
0.000000000 + x = 3.844187532 + 4.666666667
x = 3.844187532 + 4.666666667

Combine like terms: 3.844187532 + 4.666666667 = 8.510854199
x = 8.510854199

Simplifying
x = 8.510854199


Subproblem 2
x + -4.666666667 = -3.844187532

Simplifying
x + -4.666666667 = -3.844187532

Reorder the terms:
-4.666666667 + x = -3.844187532

Solving
-4.666666667 + x = -3.844187532

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '4.666666667' to each side of the equation.
-4.666666667 + 4.666666667 + x = -3.844187532 + 4.666666667

Combine like terms: -4.666666667 + 4.666666667 = 0.000000000
0.000000000 + x = -3.844187532 + 4.666666667
x = -3.844187532 + 4.666666667

Combine like terms: -3.844187532 + 4.666666667 = 0.822479135
x = 0.822479135

Simplifying
x = 0.822479135


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.510854199, 0.822479135}

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