(x-3)(x-14)=10x

Simple and best practice solution for (x-3)(x-14)=10x 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-14)=10x equation:


Simplifying
(x + -3)(x + -14) = 10x

Reorder the terms:
(-3 + x)(x + -14) = 10x

Reorder the terms:
(-3 + x)(-14 + x) = 10x

Multiply (-3 + x) * (-14 + x)
(-3(-14 + x) + x(-14 + x)) = 10x
((-14 * -3 + x * -3) + x(-14 + x)) = 10x
((42 + -3x) + x(-14 + x)) = 10x
(42 + -3x + (-14 * x + x * x)) = 10x
(42 + -3x + (-14x + x2)) = 10x

Combine like terms: -3x + -14x = -17x
(42 + -17x + x2) = 10x

Solving
42 + -17x + x2 = 10x

Solving for variable 'x'.

Reorder the terms:
42 + -17x + -10x + x2 = 10x + -10x

Combine like terms: -17x + -10x = -27x
42 + -27x + x2 = 10x + -10x

Combine like terms: 10x + -10x = 0
42 + -27x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-42' to each side of the equation.
42 + -27x + -42 + x2 = 0 + -42

Reorder the terms:
42 + -42 + -27x + x2 = 0 + -42

Combine like terms: 42 + -42 = 0
0 + -27x + x2 = 0 + -42
-27x + x2 = 0 + -42

Combine like terms: 0 + -42 = -42
-27x + x2 = -42

The x term is -27x.  Take half its coefficient (-13.5).
Square it (182.25) and add it to both sides.

Add '182.25' to each side of the equation.
-27x + 182.25 + x2 = -42 + 182.25

Reorder the terms:
182.25 + -27x + x2 = -42 + 182.25

Combine like terms: -42 + 182.25 = 140.25
182.25 + -27x + x2 = 140.25

Factor a perfect square on the left side:
(x + -13.5)(x + -13.5) = 140.25

Calculate the square root of the right side: 11.842719282

Break this problem into two subproblems by setting 
(x + -13.5) equal to 11.842719282 and -11.842719282.

Subproblem 1

x + -13.5 = 11.842719282 Simplifying x + -13.5 = 11.842719282 Reorder the terms: -13.5 + x = 11.842719282 Solving -13.5 + x = 11.842719282 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '13.5' to each side of the equation. -13.5 + 13.5 + x = 11.842719282 + 13.5 Combine like terms: -13.5 + 13.5 = 0.0 0.0 + x = 11.842719282 + 13.5 x = 11.842719282 + 13.5 Combine like terms: 11.842719282 + 13.5 = 25.342719282 x = 25.342719282 Simplifying x = 25.342719282

Subproblem 2

x + -13.5 = -11.842719282 Simplifying x + -13.5 = -11.842719282 Reorder the terms: -13.5 + x = -11.842719282 Solving -13.5 + x = -11.842719282 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '13.5' to each side of the equation. -13.5 + 13.5 + x = -11.842719282 + 13.5 Combine like terms: -13.5 + 13.5 = 0.0 0.0 + x = -11.842719282 + 13.5 x = -11.842719282 + 13.5 Combine like terms: -11.842719282 + 13.5 = 1.657280718 x = 1.657280718 Simplifying x = 1.657280718

Solution

The solution to the problem is based on the solutions from the subproblems. x = {25.342719282, 1.657280718}

See similar equations:

| 17x-3-4=10 | | 72=8(d+6) | | x+0.21x=6 | | 2343=33(p+30) | | 72=8(d+12) | | 5(g+5)=85 | | 30+4x+2-8+6x=180 | | 744=4(x+19) | | 16=3h+4 | | 10+-5y=18 | | 2w+3x-12y+7w+12x+4y= | | 0=43t-5t^2 | | h(t)=-16t^2+32t+33 | | 2x-34=26 | | 5(?-7)=3(?-4)-13 | | 7x-2x+20=40 | | 2x-2y=54 | | 9x-4-5x=7 | | x+(3+2y)+2y=8 | | y=2x^2-8x^2+6 | | 8+4x=3x+18 | | 4x-6=4x+5 | | y=24x-5 | | (3x+2)(x+3)=180 | | (3y^2-2y)+(5y^2+6y)= | | 7x=2x+15.5 | | 13j-13j+j=6 | | 4(x-10)=-6(-2-x)-6x | | 13m-7m-5m=-4 | | 70-6x=90-14x | | f(7)=-10-5 | | -5(-1x-9)=95 |

Equations solver categories