16x^2=18x-1

Simple and best practice solution for 16x^2=18x-1 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 16x^2=18x-1 equation:


Simplifying
16x2 = 18x + -1

Reorder the terms:
16x2 = -1 + 18x

Solving
16x2 = -1 + 18x

Solving for variable 'x'.

Reorder the terms:
1 + -18x + 16x2 = -1 + 18x + 1 + -18x

Reorder the terms:
1 + -18x + 16x2 = -1 + 1 + 18x + -18x

Combine like terms: -1 + 1 = 0
1 + -18x + 16x2 = 0 + 18x + -18x
1 + -18x + 16x2 = 18x + -18x

Combine like terms: 18x + -18x = 0
1 + -18x + 16x2 = 0

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

Divide each side by '16'.
0.0625 + -1.125x + x2 = 0

Move the constant term to the right:

Add '-0.0625' to each side of the equation.
0.0625 + -1.125x + -0.0625 + x2 = 0 + -0.0625

Reorder the terms:
0.0625 + -0.0625 + -1.125x + x2 = 0 + -0.0625

Combine like terms: 0.0625 + -0.0625 = 0.0000
0.0000 + -1.125x + x2 = 0 + -0.0625
-1.125x + x2 = 0 + -0.0625

Combine like terms: 0 + -0.0625 = -0.0625
-1.125x + x2 = -0.0625

The x term is -1.125x.  Take half its coefficient (-0.5625).
Square it (0.31640625) and add it to both sides.

Add '0.31640625' to each side of the equation.
-1.125x + 0.31640625 + x2 = -0.0625 + 0.31640625

Reorder the terms:
0.31640625 + -1.125x + x2 = -0.0625 + 0.31640625

Combine like terms: -0.0625 + 0.31640625 = 0.25390625
0.31640625 + -1.125x + x2 = 0.25390625

Factor a perfect square on the left side:
(x + -0.5625)(x + -0.5625) = 0.25390625

Calculate the square root of the right side: 0.503891109

Break this problem into two subproblems by setting 
(x + -0.5625) equal to 0.503891109 and -0.503891109.

Subproblem 1

x + -0.5625 = 0.503891109 Simplifying x + -0.5625 = 0.503891109 Reorder the terms: -0.5625 + x = 0.503891109 Solving -0.5625 + x = 0.503891109 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5625' to each side of the equation. -0.5625 + 0.5625 + x = 0.503891109 + 0.5625 Combine like terms: -0.5625 + 0.5625 = 0.0000 0.0000 + x = 0.503891109 + 0.5625 x = 0.503891109 + 0.5625 Combine like terms: 0.503891109 + 0.5625 = 1.066391109 x = 1.066391109 Simplifying x = 1.066391109

Subproblem 2

x + -0.5625 = -0.503891109 Simplifying x + -0.5625 = -0.503891109 Reorder the terms: -0.5625 + x = -0.503891109 Solving -0.5625 + x = -0.503891109 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5625' to each side of the equation. -0.5625 + 0.5625 + x = -0.503891109 + 0.5625 Combine like terms: -0.5625 + 0.5625 = 0.0000 0.0000 + x = -0.503891109 + 0.5625 x = -0.503891109 + 0.5625 Combine like terms: -0.503891109 + 0.5625 = 0.058608891 x = 0.058608891 Simplifying x = 0.058608891

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.066391109, 0.058608891}

See similar equations:

| -10-3x=20 | | 14=-4-3x | | -7-3x=-16 | | 5y=-8x+2 | | 0.67*0.3= | | -10=2-4x | | 0=1755-6q+q^2 | | 3y+x=4x+y-10 | | 12=-8+10x | | -6+2x=12 | | -13=8+3x | | 180=3a+(2a-25) | | 12=8-2x | | -17=-5-3x | | -19=6-5x | | 9+2x=-11 | | 3d-6=5d+6 | | 0=0.98b+0.02-b | | -2+7x=-16 | | -4d-6+7=5d+6 | | 5=3x-2x+1 | | 14=-4+3x | | 2(q-2)+2=5q-7-2q | | 180=4y+x-5+4x+y+10 | | 1.8+1.9=-1.7 | | 2(1x+4)=3(x-2) | | M-4.5=12 | | -5g-(11-2g)=-(g+g)+5 | | Z+18=54 | | 2x-x+1=4 | | 3n-25=5+n | | 5(x-2)+4(3+x)=20 |

Equations solver categories