7x^2-65x+30=

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Solution for 7x^2-65x+30= equation:


Simplifying
7x2 + -65x + 30 = 0

Reorder the terms:
30 + -65x + 7x2 = 0

Solving
30 + -65x + 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'.
4.285714286 + -9.285714286x + x2 = 0

Move the constant term to the right:

Add '-4.285714286' to each side of the equation.
4.285714286 + -9.285714286x + -4.285714286 + x2 = 0 + -4.285714286

Reorder the terms:
4.285714286 + -4.285714286 + -9.285714286x + x2 = 0 + -4.285714286

Combine like terms: 4.285714286 + -4.285714286 = 0.000000000
0.000000000 + -9.285714286x + x2 = 0 + -4.285714286
-9.285714286x + x2 = 0 + -4.285714286

Combine like terms: 0 + -4.285714286 = -4.285714286
-9.285714286x + x2 = -4.285714286

The x term is -9.285714286x.  Take half its coefficient (-4.642857143).
Square it (21.55612245) and add it to both sides.

Add '21.55612245' to each side of the equation.
-9.285714286x + 21.55612245 + x2 = -4.285714286 + 21.55612245

Reorder the terms:
21.55612245 + -9.285714286x + x2 = -4.285714286 + 21.55612245

Combine like terms: -4.285714286 + 21.55612245 = 17.270408164
21.55612245 + -9.285714286x + x2 = 17.270408164

Factor a perfect square on the left side:
(x + -4.642857143)(x + -4.642857143) = 17.270408164

Calculate the square root of the right side: 4.155768059

Break this problem into two subproblems by setting 
(x + -4.642857143) equal to 4.155768059 and -4.155768059.

Subproblem 1

x + -4.642857143 = 4.155768059 Simplifying x + -4.642857143 = 4.155768059 Reorder the terms: -4.642857143 + x = 4.155768059 Solving -4.642857143 + x = 4.155768059 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.642857143' to each side of the equation. -4.642857143 + 4.642857143 + x = 4.155768059 + 4.642857143 Combine like terms: -4.642857143 + 4.642857143 = 0.000000000 0.000000000 + x = 4.155768059 + 4.642857143 x = 4.155768059 + 4.642857143 Combine like terms: 4.155768059 + 4.642857143 = 8.798625202 x = 8.798625202 Simplifying x = 8.798625202

Subproblem 2

x + -4.642857143 = -4.155768059 Simplifying x + -4.642857143 = -4.155768059 Reorder the terms: -4.642857143 + x = -4.155768059 Solving -4.642857143 + x = -4.155768059 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.642857143' to each side of the equation. -4.642857143 + 4.642857143 + x = -4.155768059 + 4.642857143 Combine like terms: -4.642857143 + 4.642857143 = 0.000000000 0.000000000 + x = -4.155768059 + 4.642857143 x = -4.155768059 + 4.642857143 Combine like terms: -4.155768059 + 4.642857143 = 0.487089084 x = 0.487089084 Simplifying x = 0.487089084

Solution

The solution to the problem is based on the solutions from the subproblems. x = {8.798625202, 0.487089084}

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