x^2=3x+9

Simple and best practice solution for x^2=3x+9 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+9 equation:


Simplifying
x2 = 3x + 9

Reorder the terms:
x2 = 9 + 3x

Solving
x2 = 9 + 3x

Solving for variable 'x'.

Reorder the terms:
-9 + -3x + x2 = 9 + 3x + -9 + -3x

Reorder the terms:
-9 + -3x + x2 = 9 + -9 + 3x + -3x

Combine like terms: 9 + -9 = 0
-9 + -3x + x2 = 0 + 3x + -3x
-9 + -3x + x2 = 3x + -3x

Combine like terms: 3x + -3x = 0
-9 + -3x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '9' to each side of the equation.
-9 + -3x + 9 + x2 = 0 + 9

Reorder the terms:
-9 + 9 + -3x + x2 = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -3x + x2 = 0 + 9
-3x + x2 = 0 + 9

Combine like terms: 0 + 9 = 9
-3x + x2 = 9

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 = 9 + 2.25

Reorder the terms:
2.25 + -3x + x2 = 9 + 2.25

Combine like terms: 9 + 2.25 = 11.25
2.25 + -3x + x2 = 11.25

Factor a perfect square on the left side:
(x + -1.5)(x + -1.5) = 11.25

Calculate the square root of the right side: 3.354101966

Break this problem into two subproblems by setting 
(x + -1.5) equal to 3.354101966 and -3.354101966.

Subproblem 1

x + -1.5 = 3.354101966 Simplifying x + -1.5 = 3.354101966 Reorder the terms: -1.5 + x = 3.354101966 Solving -1.5 + x = 3.354101966 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 = 3.354101966 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 3.354101966 + 1.5 x = 3.354101966 + 1.5 Combine like terms: 3.354101966 + 1.5 = 4.854101966 x = 4.854101966 Simplifying x = 4.854101966

Subproblem 2

x + -1.5 = -3.354101966 Simplifying x + -1.5 = -3.354101966 Reorder the terms: -1.5 + x = -3.354101966 Solving -1.5 + x = -3.354101966 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 = -3.354101966 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -3.354101966 + 1.5 x = -3.354101966 + 1.5 Combine like terms: -3.354101966 + 1.5 = -1.854101966 x = -1.854101966 Simplifying x = -1.854101966

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4.854101966, -1.854101966}

See similar equations:

| y=-2(7)+20 | | (x-4)(x-2+5i)(x-2-5i)= | | 9+3(-2+-5)=6 | | 1.5x+x+(15+x)=190 | | 3x+5x+7x=120 | | 36/6*(2+2+2)= | | 3x+5x+7x=88 | | 13-2c=9 | | x^2+14x=24 | | 10+2(x+1)+7x=3x+1 | | 21a^2-2a-3=0 | | M-2=10 | | 6(x+2)=4-(3x-2x)-1 | | F=-9+2F | | 0=25x+76 | | 6+0.8c=0.9c | | 3x+2y-2=-8+2 | | 16b^2+5=54 | | 2x+x+10+x+18+3x+x-1+x=360 | | F(x)=-x^2-3x+12 | | .25x+.1(50-x)=-8.6 | | s=16(15)+110 | | s=16(0)+110 | | 3.2a-16=49 | | 3x+2+2x+2x+1+x+5=360 | | s=14(15)+240 | | 7x+2=-10+4x | | 1.35(t-75)=8 | | .25x+.1(50-x)=8.6 | | (-8)+12= | | s=14(0)+240 | | s=14t+240 |

Equations solver categories