5x^2-15x+1=0

Simple and best practice solution for 5x^2-15x+1=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 5x^2-15x+1=0 equation:


Simplifying
5x2 + -15x + 1 = 0

Reorder the terms:
1 + -15x + 5x2 = 0

Solving
1 + -15x + 5x2 = 0

Solving for variable 'x'.

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

Divide each side by '5'.
0.2 + -3x + x2 = 0

Move the constant term to the right:

Add '-0.2' to each side of the equation.
0.2 + -3x + -0.2 + x2 = 0 + -0.2

Reorder the terms:
0.2 + -0.2 + -3x + x2 = 0 + -0.2

Combine like terms: 0.2 + -0.2 = 0.0
0.0 + -3x + x2 = 0 + -0.2
-3x + x2 = 0 + -0.2

Combine like terms: 0 + -0.2 = -0.2
-3x + x2 = -0.2

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 = -0.2 + 2.25

Reorder the terms:
2.25 + -3x + x2 = -0.2 + 2.25

Combine like terms: -0.2 + 2.25 = 2.05
2.25 + -3x + x2 = 2.05

Factor a perfect square on the left side:
(x + -1.5)(x + -1.5) = 2.05

Calculate the square root of the right side: 1.431782106

Break this problem into two subproblems by setting 
(x + -1.5) equal to 1.431782106 and -1.431782106.

Subproblem 1

x + -1.5 = 1.431782106 Simplifying x + -1.5 = 1.431782106 Reorder the terms: -1.5 + x = 1.431782106 Solving -1.5 + x = 1.431782106 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 = 1.431782106 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 1.431782106 + 1.5 x = 1.431782106 + 1.5 Combine like terms: 1.431782106 + 1.5 = 2.931782106 x = 2.931782106 Simplifying x = 2.931782106

Subproblem 2

x + -1.5 = -1.431782106 Simplifying x + -1.5 = -1.431782106 Reorder the terms: -1.5 + x = -1.431782106 Solving -1.5 + x = -1.431782106 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 = -1.431782106 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -1.431782106 + 1.5 x = -1.431782106 + 1.5 Combine like terms: -1.431782106 + 1.5 = 0.068217894 x = 0.068217894 Simplifying x = 0.068217894

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.931782106, 0.068217894}

See similar equations:

| f(x)=-x+7 | | 2y-2(-2)=12 | | -x^2=2x-3 | | 1.3+9.4-9.03n=3.52 | | lny=1.3+.7x | | 3cos(x)+2sin(x)-xsin(x)+xcos(x)=1 | | 1.3+9.4-9.03=3.52 | | 5(9x+1)=44x+7 | | .25w+.33(500)=160 | | -11(2.78+0.3y)+10y=5 | | x=34+10 | | .25(250)+.33f=160 | | 5(9x-1)=45x+5 | | 9=2(k+1)-3(k-1) | | -9x+3y=25 | | -7x+15=-9x-1 | | 8x+-11-x=7x | | 1w+.33(500)=160 | | logQ(0)= | | 2(9x+2)=18x-4 | | 10x^2-41x=-21 | | 10kpq-q=2kp+3q | | 1(250)+.33f=160 | | 67.96+0.12x=53.96+0.14 | | 2x^2-33x+108=0 | | 50x^2+2000=30000 | | 5x-80=-x-8 | | 2/5n-3=9/5-5 | | -76+11x=100 | | 20+0.05=10+0.07 | | 7-3(c+2)=-2 | | 20x+14=22x |

Equations solver categories