x(4x-3)=2

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


Simplifying
x(4x + -3) = 2

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

Solving
-3x + 4x2 = 2

Solving for variable 'x'.

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

Combine like terms: 2 + -2 = 0
-2 + -3x + 4x2 = 0

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

Divide each side by '4'.
-0.5 + -0.75x + x2 = 0

Move the constant term to the right:

Add '0.5' to each side of the equation.
-0.5 + -0.75x + 0.5 + x2 = 0 + 0.5

Reorder the terms:
-0.5 + 0.5 + -0.75x + x2 = 0 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + -0.75x + x2 = 0 + 0.5
-0.75x + x2 = 0 + 0.5

Combine like terms: 0 + 0.5 = 0.5
-0.75x + x2 = 0.5

The x term is -0.75x.  Take half its coefficient (-0.375).
Square it (0.140625) and add it to both sides.

Add '0.140625' to each side of the equation.
-0.75x + 0.140625 + x2 = 0.5 + 0.140625

Reorder the terms:
0.140625 + -0.75x + x2 = 0.5 + 0.140625

Combine like terms: 0.5 + 0.140625 = 0.640625
0.140625 + -0.75x + x2 = 0.640625

Factor a perfect square on the left side:
(x + -0.375)(x + -0.375) = 0.640625

Calculate the square root of the right side: 0.80039053

Break this problem into two subproblems by setting 
(x + -0.375) equal to 0.80039053 and -0.80039053.

Subproblem 1

x + -0.375 = 0.80039053 Simplifying x + -0.375 = 0.80039053 Reorder the terms: -0.375 + x = 0.80039053 Solving -0.375 + x = 0.80039053 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.375' to each side of the equation. -0.375 + 0.375 + x = 0.80039053 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + x = 0.80039053 + 0.375 x = 0.80039053 + 0.375 Combine like terms: 0.80039053 + 0.375 = 1.17539053 x = 1.17539053 Simplifying x = 1.17539053

Subproblem 2

x + -0.375 = -0.80039053 Simplifying x + -0.375 = -0.80039053 Reorder the terms: -0.375 + x = -0.80039053 Solving -0.375 + x = -0.80039053 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.375' to each side of the equation. -0.375 + 0.375 + x = -0.80039053 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + x = -0.80039053 + 0.375 x = -0.80039053 + 0.375 Combine like terms: -0.80039053 + 0.375 = -0.42539053 x = -0.42539053 Simplifying x = -0.42539053

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.17539053, -0.42539053}

See similar equations:

| -3(x-2)+3=9 | | 4x^2+8x+7=4 | | 16x+42-13x=24 | | 8x-5=20x+1 | | b^2+11b+18=0 | | -28=7x | | w^2+5w-150=0 | | (10s+7)(3s-9)=0 | | -4y+1=-3(2y+3) | | 17x=10x | | d-2=6 | | 10x-16=6x-12 | | 2+m=9 | | 4x-6=3x-18 | | c-4=23 | | 4x+36=10x-40 | | 7x^2+2x+5=0 | | g(x)=x^2-5g(h+1) | | 8=-2x | | k+6=8 | | x^2+7x+15=5 | | k= | | (t+7)(t-9)=0 | | -8=x-9 | | x=h^2-3 | | 2w+2[w+90]=380 | | 14-(3m-30)=15m-10 | | w^2=4w+5 | | x-6=3x-18 | | 0.16n+3-0.4n=0.31n-0.3 | | 40=2(x+1)-10 | | 2w+2[5w+10]=380 |

Equations solver categories