7x^2-84x+72=0

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Solution for 7x^2-84x+72=0 equation:


Simplifying
7x2 + -84x + 72 = 0

Reorder the terms:
72 + -84x + 7x2 = 0

Solving
72 + -84x + 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'.
10.28571429 + -12x + x2 = 0

Move the constant term to the right:

Add '-10.28571429' to each side of the equation.
10.28571429 + -12x + -10.28571429 + x2 = 0 + -10.28571429

Reorder the terms:
10.28571429 + -10.28571429 + -12x + x2 = 0 + -10.28571429

Combine like terms: 10.28571429 + -10.28571429 = 0.00000000
0.00000000 + -12x + x2 = 0 + -10.28571429
-12x + x2 = 0 + -10.28571429

Combine like terms: 0 + -10.28571429 = -10.28571429
-12x + x2 = -10.28571429

The x term is -12x.  Take half its coefficient (-6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
-12x + 36 + x2 = -10.28571429 + 36

Reorder the terms:
36 + -12x + x2 = -10.28571429 + 36

Combine like terms: -10.28571429 + 36 = 25.71428571
36 + -12x + x2 = 25.71428571

Factor a perfect square on the left side:
(x + -6)(x + -6) = 25.71428571

Calculate the square root of the right side: 5.070925528

Break this problem into two subproblems by setting 
(x + -6) equal to 5.070925528 and -5.070925528.

Subproblem 1

x + -6 = 5.070925528 Simplifying x + -6 = 5.070925528 Reorder the terms: -6 + x = 5.070925528 Solving -6 + x = 5.070925528 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = 5.070925528 + 6 Combine like terms: -6 + 6 = 0 0 + x = 5.070925528 + 6 x = 5.070925528 + 6 Combine like terms: 5.070925528 + 6 = 11.070925528 x = 11.070925528 Simplifying x = 11.070925528

Subproblem 2

x + -6 = -5.070925528 Simplifying x + -6 = -5.070925528 Reorder the terms: -6 + x = -5.070925528 Solving -6 + x = -5.070925528 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = -5.070925528 + 6 Combine like terms: -6 + 6 = 0 0 + x = -5.070925528 + 6 x = -5.070925528 + 6 Combine like terms: -5.070925528 + 6 = 0.929074472 x = 0.929074472 Simplifying x = 0.929074472

Solution

The solution to the problem is based on the solutions from the subproblems. x = {11.070925528, 0.929074472}

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