(x-3)(x-4)=10

Simple and best practice solution for (x-3)(x-4)=10 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-3)(x-4)=10 equation: 


Simplifying
(x + -3)(x + -4) = 10

Reorder the terms:
(-3 + x)(x + -4) = 10

Reorder the terms:
(-3 + x)(-4 + x) = 10

Multiply (-3 + x) * (-4 + x)
(-3(-4 + x) + x(-4 + x)) = 10
((-4 * -3 + x * -3) + x(-4 + x)) = 10
((12 + -3x) + x(-4 + x)) = 10
(12 + -3x + (-4 * x + x * x)) = 10
(12 + -3x + (-4x + x2)) = 10

Combine like terms: -3x + -4x = -7x
(12 + -7x + x2) = 10

Solving
12 + -7x + x2 = 10

Solving for variable 'x'.

Reorder the terms:
12 + -10 + -7x + x2 = 10 + -10

Combine like terms: 12 + -10 = 2
2 + -7x + x2 = 10 + -10

Combine like terms: 10 + -10 = 0
2 + -7x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + -7x + -2 + x2 = 0 + -2

Reorder the terms:
2 + -2 + -7x + x2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -7x + x2 = 0 + -2
-7x + x2 = 0 + -2

Combine like terms: 0 + -2 = -2
-7x + x2 = -2

The x term is -7x.  Take half its coefficient (-3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
-7x + 12.25 + x2 = -2 + 12.25

Reorder the terms:
12.25 + -7x + x2 = -2 + 12.25

Combine like terms: -2 + 12.25 = 10.25
12.25 + -7x + x2 = 10.25

Factor a perfect square on the left side:
(x + -3.5)(x + -3.5) = 10.25

Calculate the square root of the right side: 3.201562119

Break this problem into two subproblems by setting 
(x + -3.5) equal to 3.201562119 and -3.201562119.


Subproblem 1
x + -3.5 = 3.201562119

Simplifying
x + -3.5 = 3.201562119

Reorder the terms:
-3.5 + x = 3.201562119

Solving
-3.5 + x = 3.201562119

Solving for variable 'x'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + x = 3.201562119 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + x = 3.201562119 + 3.5
x = 3.201562119 + 3.5

Combine like terms: 3.201562119 + 3.5 = 6.701562119
x = 6.701562119

Simplifying
x = 6.701562119


Subproblem 2
x + -3.5 = -3.201562119

Simplifying
x + -3.5 = -3.201562119

Reorder the terms:
-3.5 + x = -3.201562119

Solving
-3.5 + x = -3.201562119

Solving for variable 'x'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + x = -3.201562119 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + x = -3.201562119 + 3.5
x = -3.201562119 + 3.5

Combine like terms: -3.201562119 + 3.5 = 0.298437881
x = 0.298437881

Simplifying
x = 0.298437881


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.701562119, 0.298437881}

See similar equations:

| 12x-20=7+3x | | 3x-4=9x-22 | | 315+6-(7*2)*3= | | 0.5(6w-8)=8 | | 3ln(x-4)=-3 | | 2x^2+y+z=100 | | y/8=18 | | 3d+12=d+11 | | 3y=2xy | | 12v=48 | | 15c=45 | | 54=19-z | | 2(7+9)=2(7)+2(n) | | -(2x+4x-12)+17=9 | | Y=0.495x-973.8 | | -2(x+9)=-(6-5x)+2 | | 4x+40=15 | | (x^2z^-1)(2x^-4u/z^-3) | | 16.6576=3.88(2.2+5.8x)+4.4(1-3.1x) | | 3.1(5.1-5.8a)+2.5(a+4.2)=-29.418 | | 35b-b=306 | | (5v+3)(4+v)=0 | | tanx=-7/5 | | y=x+2x+1 | | 8g+10=15r-8 | | -51.442=-2.3(3.1r+0.9)+3.5(0.3+2.2r) | | 6(9w+8)-9=6w+567 | | 520/14*x/15 | | 6(u-1)+5u+1=5(u+6)-6 | | 8(9d-6)+10=4d+574 | | 96a-17a=60a+a | | 8(8a+2)-10=6a+528 |

Equations solver categories