x^2+3x=37

Simple and best practice solution for x^2+3x=37 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=37 equation:


Simplifying
x2 + 3x = 37

Reorder the terms:
3x + x2 = 37

Solving
3x + x2 = 37

Solving for variable 'x'.

Reorder the terms:
-37 + 3x + x2 = 37 + -37

Combine like terms: 37 + -37 = 0
-37 + 3x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '37' to each side of the equation.
-37 + 3x + 37 + x2 = 0 + 37

Reorder the terms:
-37 + 37 + 3x + x2 = 0 + 37

Combine like terms: -37 + 37 = 0
0 + 3x + x2 = 0 + 37
3x + x2 = 0 + 37

Combine like terms: 0 + 37 = 37
3x + x2 = 37

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 = 37 + 2.25

Reorder the terms:
2.25 + 3x + x2 = 37 + 2.25

Combine like terms: 37 + 2.25 = 39.25
2.25 + 3x + x2 = 39.25

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = 39.25

Calculate the square root of the right side: 6.264982043

Break this problem into two subproblems by setting 
(x + 1.5) equal to 6.264982043 and -6.264982043.

Subproblem 1

x + 1.5 = 6.264982043 Simplifying x + 1.5 = 6.264982043 Reorder the terms: 1.5 + x = 6.264982043 Solving 1.5 + x = 6.264982043 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 = 6.264982043 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 6.264982043 + -1.5 x = 6.264982043 + -1.5 Combine like terms: 6.264982043 + -1.5 = 4.764982043 x = 4.764982043 Simplifying x = 4.764982043

Subproblem 2

x + 1.5 = -6.264982043 Simplifying x + 1.5 = -6.264982043 Reorder the terms: 1.5 + x = -6.264982043 Solving 1.5 + x = -6.264982043 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 = -6.264982043 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -6.264982043 + -1.5 x = -6.264982043 + -1.5 Combine like terms: -6.264982043 + -1.5 = -7.764982043 x = -7.764982043 Simplifying x = -7.764982043

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4.764982043, -7.764982043}

See similar equations:

| 12-2x/4=10 | | x/7=a/4 | | (5v-4)(8-v)=0 | | -6x+8=3x+10 | | 10+v=-6v-4 | | -3(x-14)+2(4x+6)= | | 6r+14=7r+4+4 | | -16-a=2a-a | | 5b-9=7b+1+2 | | 1+2x-8=4x-7 | | x-(3-3x)=33 | | 13+2x-13=2x-10 | | -5(-8n-1)+3(5+n)=20 | | 8x+5=1+7x+1 | | -7(-m+7)-2(-6+2m)=-58 | | 2x^2+4x-5=2x^2-1 | | -4(k-3)+6(k+3)=40 | | -8=4(3-8k)-4(8-5k) | | qd=36-6p | | w+5.7=8.38 | | 34=-1+5x | | -54=6(a-1) | | -54=-6(1+8x) | | a(9ab+12-13ba-4(b+4))= | | -16=-8(b+3) | | f(x)=-2x^3+15x^2-31x+12 | | a^3-16a^2+80a-128=0 | | 2=2(1+6n) | | 20+2*5-y+20=24 | | N+4+6=13 | | 1/5(3x-0.5)-1/30=x/5 | | 8=-6m+7 |

Equations solver categories