-9x^2-15x+20=0

Simple and best practice solution for -9x^2-15x+20=0 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^2-15x+20=0 equation:


Simplifying
-9x2 + -15x + 20 = 0

Reorder the terms:
20 + -15x + -9x2 = 0

Solving
20 + -15x + -9x2 = 0

Solving for variable 'x'.

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

Divide each side by '-9'.
-2.222222222 + 1.666666667x + x2 = 0

Move the constant term to the right:

Add '2.222222222' to each side of the equation.
-2.222222222 + 1.666666667x + 2.222222222 + x2 = 0 + 2.222222222

Reorder the terms:
-2.222222222 + 2.222222222 + 1.666666667x + x2 = 0 + 2.222222222

Combine like terms: -2.222222222 + 2.222222222 = 0.000000000
0.000000000 + 1.666666667x + x2 = 0 + 2.222222222
1.666666667x + x2 = 0 + 2.222222222

Combine like terms: 0 + 2.222222222 = 2.222222222
1.666666667x + x2 = 2.222222222

The x term is 1.666666667x.  Take half its coefficient (0.8333333335).
Square it (0.6944444447) and add it to both sides.

Add '0.6944444447' to each side of the equation.
1.666666667x + 0.6944444447 + x2 = 2.222222222 + 0.6944444447

Reorder the terms:
0.6944444447 + 1.666666667x + x2 = 2.222222222 + 0.6944444447

Combine like terms: 2.222222222 + 0.6944444447 = 2.9166666667
0.6944444447 + 1.666666667x + x2 = 2.9166666667

Factor a perfect square on the left side:
(x + 0.8333333335)(x + 0.8333333335) = 2.9166666667

Calculate the square root of the right side: 1.707825128

Break this problem into two subproblems by setting 
(x + 0.8333333335) equal to 1.707825128 and -1.707825128.

Subproblem 1

x + 0.8333333335 = 1.707825128 Simplifying x + 0.8333333335 = 1.707825128 Reorder the terms: 0.8333333335 + x = 1.707825128 Solving 0.8333333335 + x = 1.707825128 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8333333335' to each side of the equation. 0.8333333335 + -0.8333333335 + x = 1.707825128 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + x = 1.707825128 + -0.8333333335 x = 1.707825128 + -0.8333333335 Combine like terms: 1.707825128 + -0.8333333335 = 0.8744917945 x = 0.8744917945 Simplifying x = 0.8744917945

Subproblem 2

x + 0.8333333335 = -1.707825128 Simplifying x + 0.8333333335 = -1.707825128 Reorder the terms: 0.8333333335 + x = -1.707825128 Solving 0.8333333335 + x = -1.707825128 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8333333335' to each side of the equation. 0.8333333335 + -0.8333333335 + x = -1.707825128 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + x = -1.707825128 + -0.8333333335 x = -1.707825128 + -0.8333333335 Combine like terms: -1.707825128 + -0.8333333335 = -2.5411584615 x = -2.5411584615 Simplifying x = -2.5411584615

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.8744917945, -2.5411584615}

See similar equations:

| -9x^2-15+20=0 | | (2x+6)+(-5+4)= | | 7x^2-7x-3=0 | | -42-2x=2x+13 | | 8=2x^2+4x-14 | | 3y+2x=73 | | 2/3(x+4)=1/3(2x-6) | | Tx=Sy | | 3m-2-5m=12 | | 4x-19=47 | | 4x^2-21x+37=3x+10 | | 11x+5=14x+10 | | 3+1/2(5x+2)=14 | | -3x^2-x+5=0 | | (n+2)*6=36 | | 6x+x=294 | | -15=-6+4w | | x^2+7x-3=3x+2 | | -15=-6+4e | | 24+3x=6+5x | | x^2+10x-22=5x+2 | | 0.02x=0.06x | | 4x-29=x+36 | | x^2-x-9=3 | | z/4=-7 | | -24+3x=6+5x | | 4x^2+14x+12=0 | | 6x+10+7x+15x+2=180 | | 135(x+5)=154x | | n+37=48 | | k-8=-32 | | 3x-2(k-x-1)=5x-4k |

Equations solver categories