4x^2+3x=5

Simple and best practice solution for 4x^2+3x=5 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 4x^2+3x=5 equation:


Simplifying
4x2 + 3x = 5

Reorder the terms:
3x + 4x2 = 5

Solving
3x + 4x2 = 5

Solving for variable 'x'.

Reorder the terms:
-5 + 3x + 4x2 = 5 + -5

Combine like terms: 5 + -5 = 0
-5 + 3x + 4x2 = 0

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

Divide each side by '4'.
-1.25 + 0.75x + x2 = 0

Move the constant term to the right:

Add '1.25' to each side of the equation.
-1.25 + 0.75x + 1.25 + x2 = 0 + 1.25

Reorder the terms:
-1.25 + 1.25 + 0.75x + x2 = 0 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + 0.75x + x2 = 0 + 1.25
0.75x + x2 = 0 + 1.25

Combine like terms: 0 + 1.25 = 1.25
0.75x + x2 = 1.25

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 = 1.25 + 0.140625

Reorder the terms:
0.140625 + 0.75x + x2 = 1.25 + 0.140625

Combine like terms: 1.25 + 0.140625 = 1.390625
0.140625 + 0.75x + x2 = 1.390625

Factor a perfect square on the left side:
(x + 0.375)(x + 0.375) = 1.390625

Calculate the square root of the right side: 1.179247642

Break this problem into two subproblems by setting 
(x + 0.375) equal to 1.179247642 and -1.179247642.

Subproblem 1

x + 0.375 = 1.179247642 Simplifying x + 0.375 = 1.179247642 Reorder the terms: 0.375 + x = 1.179247642 Solving 0.375 + x = 1.179247642 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 = 1.179247642 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + x = 1.179247642 + -0.375 x = 1.179247642 + -0.375 Combine like terms: 1.179247642 + -0.375 = 0.804247642 x = 0.804247642 Simplifying x = 0.804247642

Subproblem 2

x + 0.375 = -1.179247642 Simplifying x + 0.375 = -1.179247642 Reorder the terms: 0.375 + x = -1.179247642 Solving 0.375 + x = -1.179247642 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 = -1.179247642 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + x = -1.179247642 + -0.375 x = -1.179247642 + -0.375 Combine like terms: -1.179247642 + -0.375 = -1.554247642 x = -1.554247642 Simplifying x = -1.554247642

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.804247642, -1.554247642}

See similar equations:

| 12x-6x=3 | | 2x^2+48x=0 | | y=2+10x | | y=10x+2 | | 4x^2-16x+11=0 | | 5x^2=3x-2 | | 26=6y | | -6k+2k-11=-2(2k+3)-5 | | y=20-4 | | 5x+2y=49 | | 10p-6=9+8p | | 5x^2-45x=0 | | 6x^2=x+2 | | TripCost=200+25+.02x | | 2t^2+3-t+4+5t^2= | | 3(x+2)=(-15) | | -3x^2+5x-4=0 | | 14=6-4x | | -3x+14=-4 | | 2x-4(5x+6)=-6 | | 13-4c=2c-8 | | -8t-3=100 | | 2x-4(5x+6)= | | 13a-11=2 | | 15=x^2-10x+40 | | 15b+14=44 | | 15a-5=10 | | 4c-3=c+3 | | 6b+3=15 | | -6m-10=3m+8 | | 3y-16=7y+13 | | 8t-3=100 |

Equations solver categories