x^2+3x=7

Simple and best practice solution for x^2+3x=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+3x=7 equation:


Simplifying
x2 + 3x = 7

Reorder the terms:
3x + x2 = 7

Solving
3x + x2 = 7

Solving for variable 'x'.

Reorder the terms:
-7 + 3x + x2 = 7 + -7

Combine like terms: 7 + -7 = 0
-7 + 3x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '7' to each side of the equation.
-7 + 3x + 7 + x2 = 0 + 7

Reorder the terms:
-7 + 7 + 3x + x2 = 0 + 7

Combine like terms: -7 + 7 = 0
0 + 3x + x2 = 0 + 7
3x + x2 = 0 + 7

Combine like terms: 0 + 7 = 7
3x + x2 = 7

The x term is 3x.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3x + 2.25 + x2 = 7 + 2.25

Reorder the terms:
2.25 + 3x + x2 = 7 + 2.25

Combine like terms: 7 + 2.25 = 9.25
2.25 + 3x + x2 = 9.25

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = 9.25

Calculate the square root of the right side: 3.041381265

Break this problem into two subproblems by setting 
(x + 1.5) equal to 3.041381265 and -3.041381265.

Subproblem 1

x + 1.5 = 3.041381265 Simplifying x + 1.5 = 3.041381265 Reorder the terms: 1.5 + x = 3.041381265 Solving 1.5 + x = 3.041381265 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 3.041381265 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 3.041381265 + -1.5 x = 3.041381265 + -1.5 Combine like terms: 3.041381265 + -1.5 = 1.541381265 x = 1.541381265 Simplifying x = 1.541381265

Subproblem 2

x + 1.5 = -3.041381265 Simplifying x + 1.5 = -3.041381265 Reorder the terms: 1.5 + x = -3.041381265 Solving 1.5 + x = -3.041381265 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -3.041381265 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -3.041381265 + -1.5 x = -3.041381265 + -1.5 Combine like terms: -3.041381265 + -1.5 = -4.541381265 x = -4.541381265 Simplifying x = -4.541381265

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.541381265, -4.541381265}

See similar equations:

| 9x^2+6x-35=0 | | (x+6)(x+2)= | | (x^2)-6x-7=0 | | x=4y+4 | | x=4+4y | | 7-4x=16+5x | | (x^2)-18x+77=0 | | 7x-4x=16+5x | | 6(s-7)=3(4s+4) | | (x^2)+x-110=0 | | 7(2n+3)=91 | | 6(2x-7)-6=6(x-2)+6 | | x^2+14-12=0 | | 4(2f-3)+3=39 | | 6x+9=5x-7 | | 3y-6x=12 | | 8(3t+2)-60=28 | | (x^2)+2x-48=0 | | x+0.05x=126 | | x-3=23 | | 3x^2-7x+12=1 | | -1+10=3b-5-2b | | x^4+x^2-45=0 | | 4-5t+9=5t-9 | | 4x^4-22x^3-12x^2=0 | | 2(x-3)-4(x+1)+3(x-5)=2x+20 | | 3(5y-7)+2(4y+7)=0 | | 3(x+1)+2(x+2)=x+12 | | -20x-25-4x^2=0 | | x+0.09=33910 | | 12x^3+12x^2-24x=0 | | y+3=2(x+1) |

Equations solver categories