2x^2=7x+1

Simple and best practice solution for 2x^2=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 2x^2=7x+1 equation:


Simplifying
2x2 = 7x + 1

Reorder the terms:
2x2 = 1 + 7x

Solving
2x2 = 1 + 7x

Solving for variable 'x'.

Reorder the terms:
-1 + -7x + 2x2 = 1 + 7x + -1 + -7x

Reorder the terms:
-1 + -7x + 2x2 = 1 + -1 + 7x + -7x

Combine like terms: 1 + -1 = 0
-1 + -7x + 2x2 = 0 + 7x + -7x
-1 + -7x + 2x2 = 7x + -7x

Combine like terms: 7x + -7x = 0
-1 + -7x + 2x2 = 0

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

Divide each side by '2'.
-0.5 + -3.5x + x2 = 0

Move the constant term to the right:

Add '0.5' to each side of the equation.
-0.5 + -3.5x + 0.5 + x2 = 0 + 0.5

Reorder the terms:
-0.5 + 0.5 + -3.5x + x2 = 0 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + -3.5x + x2 = 0 + 0.5
-3.5x + x2 = 0 + 0.5

Combine like terms: 0 + 0.5 = 0.5
-3.5x + x2 = 0.5

The x term is -3.5x.  Take half its coefficient (-1.75).
Square it (3.0625) and add it to both sides.

Add '3.0625' to each side of the equation.
-3.5x + 3.0625 + x2 = 0.5 + 3.0625

Reorder the terms:
3.0625 + -3.5x + x2 = 0.5 + 3.0625

Combine like terms: 0.5 + 3.0625 = 3.5625
3.0625 + -3.5x + x2 = 3.5625

Factor a perfect square on the left side:
(x + -1.75)(x + -1.75) = 3.5625

Calculate the square root of the right side: 1.887458609

Break this problem into two subproblems by setting 
(x + -1.75) equal to 1.887458609 and -1.887458609.

Subproblem 1

x + -1.75 = 1.887458609 Simplifying x + -1.75 = 1.887458609 Reorder the terms: -1.75 + x = 1.887458609 Solving -1.75 + x = 1.887458609 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + x = 1.887458609 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + x = 1.887458609 + 1.75 x = 1.887458609 + 1.75 Combine like terms: 1.887458609 + 1.75 = 3.637458609 x = 3.637458609 Simplifying x = 3.637458609

Subproblem 2

x + -1.75 = -1.887458609 Simplifying x + -1.75 = -1.887458609 Reorder the terms: -1.75 + x = -1.887458609 Solving -1.75 + x = -1.887458609 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + x = -1.887458609 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + x = -1.887458609 + 1.75 x = -1.887458609 + 1.75 Combine like terms: -1.887458609 + 1.75 = -0.137458609 x = -0.137458609 Simplifying x = -0.137458609

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.637458609, -0.137458609}

See similar equations:

| -5(x+1)-11=17+7 | | 8(-8+2)=6(-8) | | 4b^2-44b+120= | | 9x^2-12x+4=19 | | 1x+4y=55 | | -2x=3y+5 | | x^2+8+16=81 | | 9-3x-5+x+15=90 | | 1234567890= | | 4w=2/e | | x^2+2x=2015 | | x^2+2x-2015=0 | | =tan(2x)cot(2x) | | Fx(2x)=2x+4y | | 2x^2+12x+k= | | 6x+6=4x-13 | | -0.3(2x-3)=0.7(-5-4x) | | x^2+16+64=4 | | G(6.4)=8t+6 | | 33=21x | | G(-6)=8t+6 | | G(2)=8t+6 | | G(t)=8t+6 | | 6w+2.9=5w-7.3 | | 6y-3y-30y=0 | | .6x+13.9=x-9.74 | | 7j+32=12-j | | y=16x+430 | | -.9x+6.65=-.7x+2.85 | | 4.4+.6x=.8 | | 9x-15=-54 | | 300x-.52=500x+.02 |

Equations solver categories