(x^2)-3x-7=0

Simple and best practice solution for (x^2)-3x-7=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 (x^2)-3x-7=0 equation: 


Simplifying
(x2) + -3x + -7 = 0
x2 + -3x + -7 = 0

Reorder the terms:
-7 + -3x + x2 = 0

Solving
-7 + -3x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '7' to each side of the equation.
-7 + -3x + 7 + x2 = 0 + 7

Reorder the terms:
-7 + 7 + -3x + x2 = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -3x + x2 = 0 + 7
-3x + x2 = 0 + 7

Combine like terms: 0 + 7 = 7
-3x + x2 = 7

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 = 7 + 2.25

Reorder the terms:
2.25 + -3x + x2 = 7 + 2.25

Combine like terms: 7 + 2.25 = 9.25
2.25 + -3x + x2 = 9.25

Factor a perfect square on the left side:
(x + -1.5)(x + -1.5) = 9.25

Calculate the square root of the right side: 3.041381265

Break this problem into two subproblems by setting 
(x + -1.5) equal to 3.041381265 and -3.041381265.


Subproblem 1
x + -1.5 = 3.041381265

Simplifying
x + -1.5 = 3.041381265

Reorder the terms:
-1.5 + x = 3.041381265

Solving
-1.5 + x = 3.041381265

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 = 3.041381265 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + x = 3.041381265 + 1.5
x = 3.041381265 + 1.5

Combine like terms: 3.041381265 + 1.5 = 4.541381265
x = 4.541381265

Simplifying
x = 4.541381265


Subproblem 2
x + -1.5 = -3.041381265

Simplifying
x + -1.5 = -3.041381265

Reorder the terms:
-1.5 + x = -3.041381265

Solving
-1.5 + x = -3.041381265

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 = -3.041381265 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + x = -3.041381265 + 1.5
x = -3.041381265 + 1.5

Combine like terms: -3.041381265 + 1.5 = -1.541381265
x = -1.541381265

Simplifying
x = -1.541381265


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.541381265, -1.541381265}

See similar equations:

| (x^2)-3x-14=0 | | 2(3-4k)=-42 | | 6(f+4)=36 | | X+0.09x=1 | | 6r^2+10r^2=0 | | 2(4e+5)=90 | | y+b=q | | 2/3*x=4 | | 30x-18=20x+14 | | 5I/7-15=5 | | (2x^2)-8x+20=0 | | 22=6x/6 | | 7x-12=3x-30 | | 10x+3=2x+35 | | 40-2.5x=260 | | -3x-6=4x-8 | | (3+u)(2u+7)=0 | | y=-1.2+2 | | 1/6(12-2b)=8 | | 80=200-3d | | -2x-3-x+7=16 | | (5)^2/9 | | 5^2/9 | | 5y=8k | | x^2-7x=-1 | | 3x=2k | | 45x-5y=5 | | 3z=53 | | -6x+7+2x=31 | | 3(2x+0.1)+3(1.03-x)=0 | | -4x+7+2x=31 | | 7-(3x+9)=4 |

Equations solver categories