4x^2-14x-21=0

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Solution for 4x^2-14x-21=0 equation:


Simplifying
4x2 + -14x + -21 = 0

Reorder the terms:
-21 + -14x + 4x2 = 0

Solving
-21 + -14x + 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 + -3.5x + x2 = 0

Move the constant term to the right:

Add '5.25' to each side of the equation.
-5.25 + -3.5x + 5.25 + x2 = 0 + 5.25

Reorder the terms:
-5.25 + 5.25 + -3.5x + x2 = 0 + 5.25

Combine like terms: -5.25 + 5.25 = 0.00
0.00 + -3.5x + x2 = 0 + 5.25
-3.5x + x2 = 0 + 5.25

Combine like terms: 0 + 5.25 = 5.25
-3.5x + x2 = 5.25

The x term is -3.5x.  Take half its coefficient (-1.75).
Square it (3.0625) and add it to both sides.

Add '3.0625' to each side of the equation.
-3.5x + 3.0625 + x2 = 5.25 + 3.0625

Reorder the terms:
3.0625 + -3.5x + x2 = 5.25 + 3.0625

Combine like terms: 5.25 + 3.0625 = 8.3125
3.0625 + -3.5x + x2 = 8.3125

Factor a perfect square on the left side:
(x + -1.75)(x + -1.75) = 8.3125

Calculate the square root of the right side: 2.883140649

Break this problem into two subproblems by setting 
(x + -1.75) equal to 2.883140649 and -2.883140649.

Subproblem 1

x + -1.75 = 2.883140649 Simplifying x + -1.75 = 2.883140649 Reorder the terms: -1.75 + x = 2.883140649 Solving -1.75 + x = 2.883140649 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + x = 2.883140649 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + x = 2.883140649 + 1.75 x = 2.883140649 + 1.75 Combine like terms: 2.883140649 + 1.75 = 4.633140649 x = 4.633140649 Simplifying x = 4.633140649

Subproblem 2

x + -1.75 = -2.883140649 Simplifying x + -1.75 = -2.883140649 Reorder the terms: -1.75 + x = -2.883140649 Solving -1.75 + x = -2.883140649 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + x = -2.883140649 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + x = -2.883140649 + 1.75 x = -2.883140649 + 1.75 Combine like terms: -2.883140649 + 1.75 = -1.133140649 x = -1.133140649 Simplifying x = -1.133140649

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4.633140649, -1.133140649}

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