21x^2=55x+14

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Solution for 21x^2=55x+14 equation:


Simplifying
21x2 = 55x + 14

Reorder the terms:
21x2 = 14 + 55x

Solving
21x2 = 14 + 55x

Solving for variable 'x'.

Reorder the terms:
-14 + -55x + 21x2 = 14 + 55x + -14 + -55x

Reorder the terms:
-14 + -55x + 21x2 = 14 + -14 + 55x + -55x

Combine like terms: 14 + -14 = 0
-14 + -55x + 21x2 = 0 + 55x + -55x
-14 + -55x + 21x2 = 55x + -55x

Combine like terms: 55x + -55x = 0
-14 + -55x + 21x2 = 0

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

Divide each side by '21'.
-0.6666666667 + -2.619047619x + x2 = 0

Move the constant term to the right:

Add '0.6666666667' to each side of the equation.
-0.6666666667 + -2.619047619x + 0.6666666667 + x2 = 0 + 0.6666666667

Reorder the terms:
-0.6666666667 + 0.6666666667 + -2.619047619x + x2 = 0 + 0.6666666667

Combine like terms: -0.6666666667 + 0.6666666667 = 0.0000000000
0.0000000000 + -2.619047619x + x2 = 0 + 0.6666666667
-2.619047619x + x2 = 0 + 0.6666666667

Combine like terms: 0 + 0.6666666667 = 0.6666666667
-2.619047619x + x2 = 0.6666666667

The x term is -2.619047619x.  Take half its coefficient (-1.30952381).
Square it (1.714852609) and add it to both sides.

Add '1.714852609' to each side of the equation.
-2.619047619x + 1.714852609 + x2 = 0.6666666667 + 1.714852609

Reorder the terms:
1.714852609 + -2.619047619x + x2 = 0.6666666667 + 1.714852609

Combine like terms: 0.6666666667 + 1.714852609 = 2.3815192757
1.714852609 + -2.619047619x + x2 = 2.3815192757

Factor a perfect square on the left side:
(x + -1.30952381)(x + -1.30952381) = 2.3815192757

Calculate the square root of the right side: 1.543217184

Break this problem into two subproblems by setting 
(x + -1.30952381) equal to 1.543217184 and -1.543217184.

Subproblem 1

x + -1.30952381 = 1.543217184 Simplifying x + -1.30952381 = 1.543217184 Reorder the terms: -1.30952381 + x = 1.543217184 Solving -1.30952381 + x = 1.543217184 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.30952381' to each side of the equation. -1.30952381 + 1.30952381 + x = 1.543217184 + 1.30952381 Combine like terms: -1.30952381 + 1.30952381 = 0.00000000 0.00000000 + x = 1.543217184 + 1.30952381 x = 1.543217184 + 1.30952381 Combine like terms: 1.543217184 + 1.30952381 = 2.852740994 x = 2.852740994 Simplifying x = 2.852740994

Subproblem 2

x + -1.30952381 = -1.543217184 Simplifying x + -1.30952381 = -1.543217184 Reorder the terms: -1.30952381 + x = -1.543217184 Solving -1.30952381 + x = -1.543217184 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.30952381' to each side of the equation. -1.30952381 + 1.30952381 + x = -1.543217184 + 1.30952381 Combine like terms: -1.30952381 + 1.30952381 = 0.00000000 0.00000000 + x = -1.543217184 + 1.30952381 x = -1.543217184 + 1.30952381 Combine like terms: -1.543217184 + 1.30952381 = -0.233693374 x = -0.233693374 Simplifying x = -0.233693374

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.852740994, -0.233693374}

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