5x(2x-3)=7x+1

Simple and best practice solution for 5x(2x-3)=7x+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 5x(2x-3)=7x+1 equation:


Simplifying
5x(2x + -3) = 7x + 1

Reorder the terms:
5x(-3 + 2x) = 7x + 1
(-3 * 5x + 2x * 5x) = 7x + 1
(-15x + 10x2) = 7x + 1

Reorder the terms:
-15x + 10x2 = 1 + 7x

Solving
-15x + 10x2 = 1 + 7x

Solving for variable 'x'.

Reorder the terms:
-1 + -15x + -7x + 10x2 = 1 + 7x + -1 + -7x

Combine like terms: -15x + -7x = -22x
-1 + -22x + 10x2 = 1 + 7x + -1 + -7x

Reorder the terms:
-1 + -22x + 10x2 = 1 + -1 + 7x + -7x

Combine like terms: 1 + -1 = 0
-1 + -22x + 10x2 = 0 + 7x + -7x
-1 + -22x + 10x2 = 7x + -7x

Combine like terms: 7x + -7x = 0
-1 + -22x + 10x2 = 0

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

Divide each side by '10'.
-0.1 + -2.2x + x2 = 0.0

Move the constant term to the right:

Add '0.1' to each side of the equation.
-0.1 + -2.2x + 0.1 + x2 = 0.0 + 0.1

Reorder the terms:
-0.1 + 0.1 + -2.2x + x2 = 0.0 + 0.1

Combine like terms: -0.1 + 0.1 = 0.0
0.0 + -2.2x + x2 = 0.0 + 0.1
-2.2x + x2 = 0.0 + 0.1

Combine like terms: 0.0 + 0.1 = 0.1
-2.2x + x2 = 0.1

The x term is -2.2x.  Take half its coefficient (-1.1).
Square it (1.21) and add it to both sides.

Add '1.21' to each side of the equation.
-2.2x + 1.21 + x2 = 0.1 + 1.21

Reorder the terms:
1.21 + -2.2x + x2 = 0.1 + 1.21

Combine like terms: 0.1 + 1.21 = 1.31
1.21 + -2.2x + x2 = 1.31

Factor a perfect square on the left side:
(x + -1.1)(x + -1.1) = 1.31

Calculate the square root of the right side: 1.144552314

Break this problem into two subproblems by setting 
(x + -1.1) equal to 1.144552314 and -1.144552314.

Subproblem 1

x + -1.1 = 1.144552314 Simplifying x + -1.1 = 1.144552314 Reorder the terms: -1.1 + x = 1.144552314 Solving -1.1 + x = 1.144552314 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.1' to each side of the equation. -1.1 + 1.1 + x = 1.144552314 + 1.1 Combine like terms: -1.1 + 1.1 = 0.0 0.0 + x = 1.144552314 + 1.1 x = 1.144552314 + 1.1 Combine like terms: 1.144552314 + 1.1 = 2.244552314 x = 2.244552314 Simplifying x = 2.244552314

Subproblem 2

x + -1.1 = -1.144552314 Simplifying x + -1.1 = -1.144552314 Reorder the terms: -1.1 + x = -1.144552314 Solving -1.1 + x = -1.144552314 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.1' to each side of the equation. -1.1 + 1.1 + x = -1.144552314 + 1.1 Combine like terms: -1.1 + 1.1 = 0.0 0.0 + x = -1.144552314 + 1.1 x = -1.144552314 + 1.1 Combine like terms: -1.144552314 + 1.1 = -0.044552314 x = -0.044552314 Simplifying x = -0.044552314

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.244552314, -0.044552314}

See similar equations:

| 3x+15=6x+10 | | 3x=-4+20-5 | | 7(5g+4)/4=59.5 | | (12b+2)-(-3b-4)= | | 12d+8=9d+17 | | 6(d+8)=-18 | | -x+10=5 | | (-4y-2)+(2y-7)= | | 7(a+5)=79.8 | | 51.2=9c-1 | | 7p=68.6 | | 2(d-8)=2 | | 3(a+3)=27 | | 3=2c-1 | | 9e-1=62 | | 5x+2/5=21/15 | | 8x=3x | | 9d+8=3d+20 | | 2(1/3)+2/3 | | 2x(x-1)=3x-28 | | 7x^2-14x-23=6x^2-23x+29 | | -72-10x=130-31x | | x-1/3=6 | | 8y+3=3Y+4y | | 9k=81 | | 6-10x=30-34x | | 124-4x=4x+26 | | 11^1/2*11^3 | | -35-(-7)= | | (9)^3/2 | | (-10)+(-5)= | | (16)^3/4 |

Equations solver categories