7x^2-41x+45=0

Simple and best practice solution for 7x^2-41x+45=0 equation. Check how easy it is, and learn it for the future. Our solution is simple, and easy to understand, so don`t hesitate to use it as a solution of your homework.

If it's not what You are looking for type in the equation solver your own equation and let us solve it.

Solution for 7x^2-41x+45=0 equation: 


Simplifying
7x2 + -41x + 45 = 0

Reorder the terms:
45 + -41x + 7x2 = 0

Solving
45 + -41x + 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'.
6.428571429 + -5.857142857x + x2 = 0

Move the constant term to the right:

Add '-6.428571429' to each side of the equation.
6.428571429 + -5.857142857x + -6.428571429 + x2 = 0 + -6.428571429

Reorder the terms:
6.428571429 + -6.428571429 + -5.857142857x + x2 = 0 + -6.428571429

Combine like terms: 6.428571429 + -6.428571429 = 0.000000000
0.000000000 + -5.857142857x + x2 = 0 + -6.428571429
-5.857142857x + x2 = 0 + -6.428571429

Combine like terms: 0 + -6.428571429 = -6.428571429
-5.857142857x + x2 = -6.428571429

The x term is -5.857142857x.  Take half its coefficient (-2.928571429).
Square it (8.576530615) and add it to both sides.

Add '8.576530615' to each side of the equation.
-5.857142857x + 8.576530615 + x2 = -6.428571429 + 8.576530615

Reorder the terms:
8.576530615 + -5.857142857x + x2 = -6.428571429 + 8.576530615

Combine like terms: -6.428571429 + 8.576530615 = 2.147959186
8.576530615 + -5.857142857x + x2 = 2.147959186

Factor a perfect square on the left side:
(x + -2.928571429)(x + -2.928571429) = 2.147959186

Calculate the square root of the right side: 1.465591753

Break this problem into two subproblems by setting 
(x + -2.928571429) equal to 1.465591753 and -1.465591753.


Subproblem 1
x + -2.928571429 = 1.465591753

Simplifying
x + -2.928571429 = 1.465591753

Reorder the terms:
-2.928571429 + x = 1.465591753

Solving
-2.928571429 + x = 1.465591753

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '2.928571429' to each side of the equation.
-2.928571429 + 2.928571429 + x = 1.465591753 + 2.928571429

Combine like terms: -2.928571429 + 2.928571429 = 0.000000000
0.000000000 + x = 1.465591753 + 2.928571429
x = 1.465591753 + 2.928571429

Combine like terms: 1.465591753 + 2.928571429 = 4.394163182
x = 4.394163182

Simplifying
x = 4.394163182


Subproblem 2
x + -2.928571429 = -1.465591753

Simplifying
x + -2.928571429 = -1.465591753

Reorder the terms:
-2.928571429 + x = -1.465591753

Solving
-2.928571429 + x = -1.465591753

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '2.928571429' to each side of the equation.
-2.928571429 + 2.928571429 + x = -1.465591753 + 2.928571429

Combine like terms: -2.928571429 + 2.928571429 = 0.000000000
0.000000000 + x = -1.465591753 + 2.928571429
x = -1.465591753 + 2.928571429

Combine like terms: -1.465591753 + 2.928571429 = 1.462979676
x = 1.462979676

Simplifying
x = 1.462979676


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.394163182, 1.462979676}

See similar equations:

| 65/185 | | C^2+4c-7=0 | | -5x^2+10x-2=0 | | 2xsquared+-25-13= | | log(7x+8)=1+log(x-2) | | R^2-12t+20=0 | | 3a+2b=300 | | X^2-9/4x-25=0 | | 2xsquared-25x-13= | | 3x-6=30-9x | | 6(u-6)=8u-42 | | 2k(k-1)=12 | | 2b^2-4b=0 | | 2b^2=4b | | x^2-2x-3=45 | | 8x+10x=-3 | | y=x^2+16x-80 | | (x+-3)(x+5)+-9=0 | | (x-3)(x+5)-9=9 | | 7y-4=15-3y | | R^2-4t=0 | | x+(x-1)+(x-2)+(x-3)=14 | | 1/8x5/6 | | 11x+17y=6800 | | -8(0.1x+0.3)-2.5=0.1 | | q^2+q-30=0 | | v^2+8v+7=p | | 10r-20+2r+12=180 | | 0=25x^2-16 | | x-27.7=-17 | | -6-2=14y-9-13y | | arccos(x)-2arcsin(1/2)=pi/2 |

Equations solver categories