15x^2-90x+16=0

Simple and best practice solution for 15x^2-90x+16=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 15x^2-90x+16=0 equation:


Simplifying
15x2 + -90x + 16 = 0

Reorder the terms:
16 + -90x + 15x2 = 0

Solving
16 + -90x + 15x2 = 0

Solving for variable 'x'.

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

Divide each side by '15'.
1.066666667 + -6x + x2 = 0

Move the constant term to the right:

Add '-1.066666667' to each side of the equation.
1.066666667 + -6x + -1.066666667 + x2 = 0 + -1.066666667

Reorder the terms:
1.066666667 + -1.066666667 + -6x + x2 = 0 + -1.066666667

Combine like terms: 1.066666667 + -1.066666667 = 0.000000000
0.000000000 + -6x + x2 = 0 + -1.066666667
-6x + x2 = 0 + -1.066666667

Combine like terms: 0 + -1.066666667 = -1.066666667
-6x + x2 = -1.066666667

The x term is -6x.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6x + 9 + x2 = -1.066666667 + 9

Reorder the terms:
9 + -6x + x2 = -1.066666667 + 9

Combine like terms: -1.066666667 + 9 = 7.933333333
9 + -6x + x2 = 7.933333333

Factor a perfect square on the left side:
(x + -3)(x + -3) = 7.933333333

Calculate the square root of the right side: 2.816617357

Break this problem into two subproblems by setting 
(x + -3) equal to 2.816617357 and -2.816617357.

Subproblem 1

x + -3 = 2.816617357 Simplifying x + -3 = 2.816617357 Reorder the terms: -3 + x = 2.816617357 Solving -3 + x = 2.816617357 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 2.816617357 + 3 Combine like terms: -3 + 3 = 0 0 + x = 2.816617357 + 3 x = 2.816617357 + 3 Combine like terms: 2.816617357 + 3 = 5.816617357 x = 5.816617357 Simplifying x = 5.816617357

Subproblem 2

x + -3 = -2.816617357 Simplifying x + -3 = -2.816617357 Reorder the terms: -3 + x = -2.816617357 Solving -3 + x = -2.816617357 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -2.816617357 + 3 Combine like terms: -3 + 3 = 0 0 + x = -2.816617357 + 3 x = -2.816617357 + 3 Combine like terms: -2.816617357 + 3 = 0.183382643 x = 0.183382643 Simplifying x = 0.183382643

Solution

The solution to the problem is based on the solutions from the subproblems. x = {5.816617357, 0.183382643}

See similar equations:

| 8-(-14)= | | 4x^2-12a+9=9 | | 4a^3b^2c+68a^2b^2c+280ab^2c= | | 4(7)-4x=4 | | 4sin(x)+2=0 | | (6x^2-3x^3)-(-9x^2-9x^3)= | | 33+-23= | | 2(x-4)=10+2x-18 | | 26x^2+10x=0 | | 4a^5-8a^4-96a^3= | | 9x^2+90x+189=0 | | 6r^3+42r^2-180r= | | 9(z+4)-2(z-3)=3(z-4)+3(z-4) | | x*4-7=25 | | -6x-25(x+4)=-6(5x+2) | | 33x-2+13x-2=180 | | 6(4x-7)-3=6(x-3)+99 | | 2x^2-20x+40=2x-8 | | 6(x+15)=2x+70 | | k^2-5k-24= | | m^2+2m-63= | | -7(1+5x)+x=-(3x+7) | | 6x=4+22 | | 5x-10=x+48 | | k^2-15k+54= | | 12p+5=45 | | -10=5(2b+4) | | 12p-5=45 | | 7(y+5)= | | 10(z+1)-3(z-4)=4(z-3)+2(z-1) | | V^2-8V-2=0 | | 180-3x=x+12 |

Equations solver categories