7x^2-26x=11

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Solution for 7x^2-26x=11 equation:


Simplifying
7x2 + -26x = 11

Reorder the terms:
-26x + 7x2 = 11

Solving
-26x + 7x2 = 11

Solving for variable 'x'.

Reorder the terms:
-11 + -26x + 7x2 = 11 + -11

Combine like terms: 11 + -11 = 0
-11 + -26x + 7x2 = 0

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

Divide each side by '7'.
-1.571428571 + -3.714285714x + x2 = 0

Move the constant term to the right:

Add '1.571428571' to each side of the equation.
-1.571428571 + -3.714285714x + 1.571428571 + x2 = 0 + 1.571428571

Reorder the terms:
-1.571428571 + 1.571428571 + -3.714285714x + x2 = 0 + 1.571428571

Combine like terms: -1.571428571 + 1.571428571 = 0.000000000
0.000000000 + -3.714285714x + x2 = 0 + 1.571428571
-3.714285714x + x2 = 0 + 1.571428571

Combine like terms: 0 + 1.571428571 = 1.571428571
-3.714285714x + x2 = 1.571428571

The x term is -3.714285714x.  Take half its coefficient (-1.857142857).
Square it (3.448979591) and add it to both sides.

Add '3.448979591' to each side of the equation.
-3.714285714x + 3.448979591 + x2 = 1.571428571 + 3.448979591

Reorder the terms:
3.448979591 + -3.714285714x + x2 = 1.571428571 + 3.448979591

Combine like terms: 1.571428571 + 3.448979591 = 5.020408162
3.448979591 + -3.714285714x + x2 = 5.020408162

Factor a perfect square on the left side:
(x + -1.857142857)(x + -1.857142857) = 5.020408162

Calculate the square root of the right side: 2.240626734

Break this problem into two subproblems by setting 
(x + -1.857142857) equal to 2.240626734 and -2.240626734.

Subproblem 1

x + -1.857142857 = 2.240626734 Simplifying x + -1.857142857 = 2.240626734 Reorder the terms: -1.857142857 + x = 2.240626734 Solving -1.857142857 + x = 2.240626734 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.857142857' to each side of the equation. -1.857142857 + 1.857142857 + x = 2.240626734 + 1.857142857 Combine like terms: -1.857142857 + 1.857142857 = 0.000000000 0.000000000 + x = 2.240626734 + 1.857142857 x = 2.240626734 + 1.857142857 Combine like terms: 2.240626734 + 1.857142857 = 4.097769591 x = 4.097769591 Simplifying x = 4.097769591

Subproblem 2

x + -1.857142857 = -2.240626734 Simplifying x + -1.857142857 = -2.240626734 Reorder the terms: -1.857142857 + x = -2.240626734 Solving -1.857142857 + x = -2.240626734 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.857142857' to each side of the equation. -1.857142857 + 1.857142857 + x = -2.240626734 + 1.857142857 Combine like terms: -1.857142857 + 1.857142857 = 0.000000000 0.000000000 + x = -2.240626734 + 1.857142857 x = -2.240626734 + 1.857142857 Combine like terms: -2.240626734 + 1.857142857 = -0.383483877 x = -0.383483877 Simplifying x = -0.383483877

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4.097769591, -0.383483877}

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