(2x-7)*(x-7)=16

Simple and best practice solution for (2x-7)*(x-7)=16 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 (2x-7)*(x-7)=16 equation:


Simplifying
(2x + -7)(x + -7) = 16

Reorder the terms:
(-7 + 2x)(x + -7) = 16

Reorder the terms:
(-7 + 2x)(-7 + x) = 16

Multiply (-7 + 2x) * (-7 + x)
(-7(-7 + x) + 2x * (-7 + x)) = 16
((-7 * -7 + x * -7) + 2x * (-7 + x)) = 16
((49 + -7x) + 2x * (-7 + x)) = 16
(49 + -7x + (-7 * 2x + x * 2x)) = 16
(49 + -7x + (-14x + 2x2)) = 16

Combine like terms: -7x + -14x = -21x
(49 + -21x + 2x2) = 16

Solving
49 + -21x + 2x2 = 16

Solving for variable 'x'.

Reorder the terms:
49 + -16 + -21x + 2x2 = 16 + -16

Combine like terms: 49 + -16 = 33
33 + -21x + 2x2 = 16 + -16

Combine like terms: 16 + -16 = 0
33 + -21x + 2x2 = 0

Begin completing the square.  Divide all terms by
2 the coefficient of the squared term: 

Divide each side by '2'.
16.5 + -10.5x + x2 = 0

Move the constant term to the right:

Add '-16.5' to each side of the equation.
16.5 + -10.5x + -16.5 + x2 = 0 + -16.5

Reorder the terms:
16.5 + -16.5 + -10.5x + x2 = 0 + -16.5

Combine like terms: 16.5 + -16.5 = 0.0
0.0 + -10.5x + x2 = 0 + -16.5
-10.5x + x2 = 0 + -16.5

Combine like terms: 0 + -16.5 = -16.5
-10.5x + x2 = -16.5

The x term is -10.5x.  Take half its coefficient (-5.25).
Square it (27.5625) and add it to both sides.

Add '27.5625' to each side of the equation.
-10.5x + 27.5625 + x2 = -16.5 + 27.5625

Reorder the terms:
27.5625 + -10.5x + x2 = -16.5 + 27.5625

Combine like terms: -16.5 + 27.5625 = 11.0625
27.5625 + -10.5x + x2 = 11.0625

Factor a perfect square on the left side:
(x + -5.25)(x + -5.25) = 11.0625

Calculate the square root of the right side: 3.326033674

Break this problem into two subproblems by setting 
(x + -5.25) equal to 3.326033674 and -3.326033674.

Subproblem 1

x + -5.25 = 3.326033674 Simplifying x + -5.25 = 3.326033674 Reorder the terms: -5.25 + x = 3.326033674 Solving -5.25 + x = 3.326033674 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.25' to each side of the equation. -5.25 + 5.25 + x = 3.326033674 + 5.25 Combine like terms: -5.25 + 5.25 = 0.00 0.00 + x = 3.326033674 + 5.25 x = 3.326033674 + 5.25 Combine like terms: 3.326033674 + 5.25 = 8.576033674 x = 8.576033674 Simplifying x = 8.576033674

Subproblem 2

x + -5.25 = -3.326033674 Simplifying x + -5.25 = -3.326033674 Reorder the terms: -5.25 + x = -3.326033674 Solving -5.25 + x = -3.326033674 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.25' to each side of the equation. -5.25 + 5.25 + x = -3.326033674 + 5.25 Combine like terms: -5.25 + 5.25 = 0.00 0.00 + x = -3.326033674 + 5.25 x = -3.326033674 + 5.25 Combine like terms: -3.326033674 + 5.25 = 1.923966326 x = 1.923966326 Simplifying x = 1.923966326

Solution

The solution to the problem is based on the solutions from the subproblems. x = {8.576033674, 1.923966326}

See similar equations:

| 2y+-10=-4 | | Y/4-15=35 | | 9.75x+9=13.5x+12 | | 14/20=35/x | | j-36/8=7 | | 6-(4z-8)=1-5z | | 3x-6+2=5x-2 | | -6x^2+600= | | 7w=w+54 | | (x)+(x+1)+(x+3)=72 | | -9+3x= | | 2w+2*(4w)=130 | | -2/5r= | | 13y=45+8y | | p+2=-8 | | 7x-34=-70 | | 6x^2=-19-15 | | 28.25+18r=19.85+32 | | 12x-13=49 | | 10-8a=-46 | | 3v=8+v | | -2z+7=1 | | N-20=-23 | | 3(x+1)2-4=5 | | 4/3h= | | 3x+17=x-1 | | 19x-24=-79 | | (-12-4)+(-4+6)*2= | | 3g+5=4 | | 6=1/6(6-3x)-5/3 | | 8w-2w=30 | | 19x-24-4x=-79 |

Equations solver categories