9x^2+30x=25

Simple and best practice solution for 9x^2+30x=25 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 9x^2+30x=25 equation:


Simplifying
9x2 + 30x = 25

Reorder the terms:
30x + 9x2 = 25

Solving
30x + 9x2 = 25

Solving for variable 'x'.

Reorder the terms:
-25 + 30x + 9x2 = 25 + -25

Combine like terms: 25 + -25 = 0
-25 + 30x + 9x2 = 0

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

Divide each side by '9'.
-2.777777778 + 3.333333333x + x2 = 0

Move the constant term to the right:

Add '2.777777778' to each side of the equation.
-2.777777778 + 3.333333333x + 2.777777778 + x2 = 0 + 2.777777778

Reorder the terms:
-2.777777778 + 2.777777778 + 3.333333333x + x2 = 0 + 2.777777778

Combine like terms: -2.777777778 + 2.777777778 = 0.000000000
0.000000000 + 3.333333333x + x2 = 0 + 2.777777778
3.333333333x + x2 = 0 + 2.777777778

Combine like terms: 0 + 2.777777778 = 2.777777778
3.333333333x + x2 = 2.777777778

The x term is 3.333333333x.  Take half its coefficient (1.666666667).
Square it (2.777777779) and add it to both sides.

Add '2.777777779' to each side of the equation.
3.333333333x + 2.777777779 + x2 = 2.777777778 + 2.777777779

Reorder the terms:
2.777777779 + 3.333333333x + x2 = 2.777777778 + 2.777777779

Combine like terms: 2.777777778 + 2.777777779 = 5.555555557
2.777777779 + 3.333333333x + x2 = 5.555555557

Factor a perfect square on the left side:
(x + 1.666666667)(x + 1.666666667) = 5.555555557

Calculate the square root of the right side: 2.357022604

Break this problem into two subproblems by setting 
(x + 1.666666667) equal to 2.357022604 and -2.357022604.

Subproblem 1

x + 1.666666667 = 2.357022604 Simplifying x + 1.666666667 = 2.357022604 Reorder the terms: 1.666666667 + x = 2.357022604 Solving 1.666666667 + x = 2.357022604 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.666666667' to each side of the equation. 1.666666667 + -1.666666667 + x = 2.357022604 + -1.666666667 Combine like terms: 1.666666667 + -1.666666667 = 0.000000000 0.000000000 + x = 2.357022604 + -1.666666667 x = 2.357022604 + -1.666666667 Combine like terms: 2.357022604 + -1.666666667 = 0.690355937 x = 0.690355937 Simplifying x = 0.690355937

Subproblem 2

x + 1.666666667 = -2.357022604 Simplifying x + 1.666666667 = -2.357022604 Reorder the terms: 1.666666667 + x = -2.357022604 Solving 1.666666667 + x = -2.357022604 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.666666667' to each side of the equation. 1.666666667 + -1.666666667 + x = -2.357022604 + -1.666666667 Combine like terms: 1.666666667 + -1.666666667 = 0.000000000 0.000000000 + x = -2.357022604 + -1.666666667 x = -2.357022604 + -1.666666667 Combine like terms: -2.357022604 + -1.666666667 = -4.023689271 x = -4.023689271 Simplifying x = -4.023689271

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.690355937, -4.023689271}

See similar equations:

| 22(g-2)=2g+8 | | 17+3=5w-w | | x^3+8x^2-25x-200=0 | | 2x+2(x+30)=800 | | 5y+17=63 | | 4x+(-3)=-11 | | -8v=7/3 | | 50=5x+y | | f=9/5c-32 | | 4x+8[x-3]=-4+8x | | 12c^2+19c-21=0 | | 22-3x-4=x/4 | | x(2)=30-13x | | -3+6+5a=7a-8a | | 5x+4(-6x+17)=-65 | | 5/2x+31/2x+15 | | 26-13a=13a-26 | | -5(t^2-2t-10)=0 | | 40-8n=-8[2n+1] | | 4(x+1)3(x-3)=2 | | -14=7x/6 | | x/6-2.3=-21.5 | | 4x^2+10x=16 | | -7x+4-3x=-76 | | x/6-2.3=21.5 | | 6x-3y=16 | | y/4=y/3-3 | | (1/6)(6t-7)=(t+7)/12 | | 2(6d+3)=18-3(-3d+16) | | 2(3x-3)=3(2x+4) | | y-5=5 | | 13w=-13w |

Equations solver categories