x(4x-3)=(2x-1)2

Simple and best practice solution for x(4x-3)=(2x-1)2 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(4x-3)=(2x-1)2 equation:


Simplifying
x(4x + -3) = (2x + -1) * 2

Reorder the terms:
x(-3 + 4x) = (2x + -1) * 2
(-3 * x + 4x * x) = (2x + -1) * 2
(-3x + 4x2) = (2x + -1) * 2

Reorder the terms:
-3x + 4x2 = (-1 + 2x) * 2

Reorder the terms for easier multiplication:
-3x + 4x2 = 2(-1 + 2x)
-3x + 4x2 = (-1 * 2 + 2x * 2)
-3x + 4x2 = (-2 + 4x)

Solving
-3x + 4x2 = -2 + 4x

Solving for variable 'x'.

Reorder the terms:
2 + -3x + -4x + 4x2 = -2 + 4x + 2 + -4x

Combine like terms: -3x + -4x = -7x
2 + -7x + 4x2 = -2 + 4x + 2 + -4x

Reorder the terms:
2 + -7x + 4x2 = -2 + 2 + 4x + -4x

Combine like terms: -2 + 2 = 0
2 + -7x + 4x2 = 0 + 4x + -4x
2 + -7x + 4x2 = 4x + -4x

Combine like terms: 4x + -4x = 0
2 + -7x + 4x2 = 0

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

Divide each side by '4'.
0.5 + -1.75x + x2 = 0

Move the constant term to the right:

Add '-0.5' to each side of the equation.
0.5 + -1.75x + -0.5 + x2 = 0 + -0.5

Reorder the terms:
0.5 + -0.5 + -1.75x + x2 = 0 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + -1.75x + x2 = 0 + -0.5
-1.75x + x2 = 0 + -0.5

Combine like terms: 0 + -0.5 = -0.5
-1.75x + x2 = -0.5

The x term is -1.75x.  Take half its coefficient (-0.875).
Square it (0.765625) and add it to both sides.

Add '0.765625' to each side of the equation.
-1.75x + 0.765625 + x2 = -0.5 + 0.765625

Reorder the terms:
0.765625 + -1.75x + x2 = -0.5 + 0.765625

Combine like terms: -0.5 + 0.765625 = 0.265625
0.765625 + -1.75x + x2 = 0.265625

Factor a perfect square on the left side:
(x + -0.875)(x + -0.875) = 0.265625

Calculate the square root of the right side: 0.515388203

Break this problem into two subproblems by setting 
(x + -0.875) equal to 0.515388203 and -0.515388203.

Subproblem 1

x + -0.875 = 0.515388203 Simplifying x + -0.875 = 0.515388203 Reorder the terms: -0.875 + x = 0.515388203 Solving -0.875 + x = 0.515388203 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.875' to each side of the equation. -0.875 + 0.875 + x = 0.515388203 + 0.875 Combine like terms: -0.875 + 0.875 = 0.000 0.000 + x = 0.515388203 + 0.875 x = 0.515388203 + 0.875 Combine like terms: 0.515388203 + 0.875 = 1.390388203 x = 1.390388203 Simplifying x = 1.390388203

Subproblem 2

x + -0.875 = -0.515388203 Simplifying x + -0.875 = -0.515388203 Reorder the terms: -0.875 + x = -0.515388203 Solving -0.875 + x = -0.515388203 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.875' to each side of the equation. -0.875 + 0.875 + x = -0.515388203 + 0.875 Combine like terms: -0.875 + 0.875 = 0.000 0.000 + x = -0.515388203 + 0.875 x = -0.515388203 + 0.875 Combine like terms: -0.515388203 + 0.875 = 0.359611797 x = 0.359611797 Simplifying x = 0.359611797

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.390388203, 0.359611797}

See similar equations:

| x-x=10 | | 7w=84 | | 24x^2+4x-4=0 | | 1+4x=33 | | 5(2x-3)=6(x-1)+4x | | .25*-7+3=x | | 4n=16(n+12) | | 25c^2-80c+64=0 | | -3x-42= | | 7-3x=-2 | | x^3+10x^2=0 | | 2(1-4n)=34-4n | | 4y=2.6 | | 3x-2(-6-11)=-113 | | 15(k+3)-k=20 | | 3x+7+6x+20=90 | | 8x^2+112x=0 | | 3x-2+6x=-56 | | 2(x+y)+6n(x+y)=0 | | 5x^2-5xy= | | 2(2c+10)-c=-13 | | 3x+9=3x+9 | | 6(x-6)+4=8(x+2)-6 | | 0=16a^2-8a-3 | | -6a=21 | | 4u^2-1=0 | | y=y | | -18+24+(-14)= | | 0-3=x | | 20+2x=-(x-4)+5x | | -6-3=x | | 4n+5-9n=5(n+2)-10n |

Equations solver categories