7x^2+21x-64=0

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Solution for 7x^2+21x-64=0 equation:


Simplifying
7x2 + 21x + -64 = 0

Reorder the terms:
-64 + 21x + 7x2 = 0

Solving
-64 + 21x + 7x2 = 0

Solving for variable 'x'.

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

Divide each side by '7'.
-9.142857143 + 3x + x2 = 0

Move the constant term to the right:

Add '9.142857143' to each side of the equation.
-9.142857143 + 3x + 9.142857143 + x2 = 0 + 9.142857143

Reorder the terms:
-9.142857143 + 9.142857143 + 3x + x2 = 0 + 9.142857143

Combine like terms: -9.142857143 + 9.142857143 = 0.000000000
0.000000000 + 3x + x2 = 0 + 9.142857143
3x + x2 = 0 + 9.142857143

Combine like terms: 0 + 9.142857143 = 9.142857143
3x + x2 = 9.142857143

The x term is 3x.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3x + 2.25 + x2 = 9.142857143 + 2.25

Reorder the terms:
2.25 + 3x + x2 = 9.142857143 + 2.25

Combine like terms: 9.142857143 + 2.25 = 11.392857143
2.25 + 3x + x2 = 11.392857143

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = 11.392857143

Calculate the square root of the right side: 3.375330672

Break this problem into two subproblems by setting 
(x + 1.5) equal to 3.375330672 and -3.375330672.

Subproblem 1

x + 1.5 = 3.375330672 Simplifying x + 1.5 = 3.375330672 Reorder the terms: 1.5 + x = 3.375330672 Solving 1.5 + x = 3.375330672 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 3.375330672 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 3.375330672 + -1.5 x = 3.375330672 + -1.5 Combine like terms: 3.375330672 + -1.5 = 1.875330672 x = 1.875330672 Simplifying x = 1.875330672

Subproblem 2

x + 1.5 = -3.375330672 Simplifying x + 1.5 = -3.375330672 Reorder the terms: 1.5 + x = -3.375330672 Solving 1.5 + x = -3.375330672 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -3.375330672 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -3.375330672 + -1.5 x = -3.375330672 + -1.5 Combine like terms: -3.375330672 + -1.5 = -4.875330672 x = -4.875330672 Simplifying x = -4.875330672

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.875330672, -4.875330672}

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