-4x^2+23x-21=0

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Solution for -4x^2+23x-21=0 equation:


Simplifying
-4x2 + 23x + -21 = 0

Reorder the terms:
-21 + 23x + -4x2 = 0

Solving
-21 + 23x + -4x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-4 the coefficient of the squared term: 

Divide each side by '-4'.
5.25 + -5.75x + x2 = 0

Move the constant term to the right:

Add '-5.25' to each side of the equation.
5.25 + -5.75x + -5.25 + x2 = 0 + -5.25

Reorder the terms:
5.25 + -5.25 + -5.75x + x2 = 0 + -5.25

Combine like terms: 5.25 + -5.25 = 0.00
0.00 + -5.75x + x2 = 0 + -5.25
-5.75x + x2 = 0 + -5.25

Combine like terms: 0 + -5.25 = -5.25
-5.75x + x2 = -5.25

The x term is -5.75x.  Take half its coefficient (-2.875).
Square it (8.265625) and add it to both sides.

Add '8.265625' to each side of the equation.
-5.75x + 8.265625 + x2 = -5.25 + 8.265625

Reorder the terms:
8.265625 + -5.75x + x2 = -5.25 + 8.265625

Combine like terms: -5.25 + 8.265625 = 3.015625
8.265625 + -5.75x + x2 = 3.015625

Factor a perfect square on the left side:
(x + -2.875)(x + -2.875) = 3.015625

Calculate the square root of the right side: 1.736555499

Break this problem into two subproblems by setting 
(x + -2.875) equal to 1.736555499 and -1.736555499.

Subproblem 1

x + -2.875 = 1.736555499 Simplifying x + -2.875 = 1.736555499 Reorder the terms: -2.875 + x = 1.736555499 Solving -2.875 + x = 1.736555499 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.875' to each side of the equation. -2.875 + 2.875 + x = 1.736555499 + 2.875 Combine like terms: -2.875 + 2.875 = 0.000 0.000 + x = 1.736555499 + 2.875 x = 1.736555499 + 2.875 Combine like terms: 1.736555499 + 2.875 = 4.611555499 x = 4.611555499 Simplifying x = 4.611555499

Subproblem 2

x + -2.875 = -1.736555499 Simplifying x + -2.875 = -1.736555499 Reorder the terms: -2.875 + x = -1.736555499 Solving -2.875 + x = -1.736555499 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.875' to each side of the equation. -2.875 + 2.875 + x = -1.736555499 + 2.875 Combine like terms: -2.875 + 2.875 = 0.000 0.000 + x = -1.736555499 + 2.875 x = -1.736555499 + 2.875 Combine like terms: -1.736555499 + 2.875 = 1.138444501 x = 1.138444501 Simplifying x = 1.138444501

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4.611555499, 1.138444501}

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