x^2+2x=7

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


Simplifying
x2 + 2x = 7

Reorder the terms:
2x + x2 = 7

Solving
2x + x2 = 7

Solving for variable 'x'.

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

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

Begin completing the square.

Move the constant term to the right:

Add '7' to each side of the equation.
-7 + 2x + 7 + x2 = 0 + 7

Reorder the terms:
-7 + 7 + 2x + x2 = 0 + 7

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

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

The x term is 2x.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2x + 1 + x2 = 7 + 1

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

Combine like terms: 7 + 1 = 8
1 + 2x + x2 = 8

Factor a perfect square on the left side:
(x + 1)(x + 1) = 8

Calculate the square root of the right side: 2.828427125

Break this problem into two subproblems by setting 
(x + 1) equal to 2.828427125 and -2.828427125.

Subproblem 1

x + 1 = 2.828427125 Simplifying x + 1 = 2.828427125 Reorder the terms: 1 + x = 2.828427125 Solving 1 + x = 2.828427125 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 2.828427125 + -1 Combine like terms: 1 + -1 = 0 0 + x = 2.828427125 + -1 x = 2.828427125 + -1 Combine like terms: 2.828427125 + -1 = 1.828427125 x = 1.828427125 Simplifying x = 1.828427125

Subproblem 2

x + 1 = -2.828427125 Simplifying x + 1 = -2.828427125 Reorder the terms: 1 + x = -2.828427125 Solving 1 + x = -2.828427125 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -2.828427125 + -1 Combine like terms: 1 + -1 = 0 0 + x = -2.828427125 + -1 x = -2.828427125 + -1 Combine like terms: -2.828427125 + -1 = -3.828427125 x = -3.828427125 Simplifying x = -3.828427125

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.828427125, -3.828427125}

See similar equations:

| 2m-3=m-5 | | 4x-24=20 | | -4-10y=10y+4 | | 84=4w | | 7-3m=-2+7m | | 5.1=0.05+0.75y | | 24=3 | | -4+2n=-7+10n | | -9+8k=4+10k | | x=0.05+0.75y | | a+b=6 | | 3+4k=-k-2 | | b+a=6 | | 2=40x-30y | | -a+6=9a+3 | | v-10=u | | 3=4 | | 2x-4y-8=0 | | -8+8m=2+10m | | 7n+5(n-3)=13n | | 4x-4y=20 | | -3-6k=-10-7k | | 8x+6y=96 | | 4x^2-15x=0 | | -4k+7=-6k-7 | | x=5.3y | | 7p+8-5p=16 | | 5+10a=7+5a | | 10x-4y-40=0 | | x^2+4x-60= | | 6x-15y=30 | | -8+a=-6+6a |

Equations solver categories