13x^2-5x-21=0

Simple and best practice solution for 13x^2-5x-21=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 13x^2-5x-21=0 equation:


Simplifying
13x2 + -5x + -21 = 0

Reorder the terms:
-21 + -5x + 13x2 = 0

Solving
-21 + -5x + 13x2 = 0

Solving for variable 'x'.

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

Divide each side by '13'.
-1.615384615 + -0.3846153846x + x2 = 0

Move the constant term to the right:

Add '1.615384615' to each side of the equation.
-1.615384615 + -0.3846153846x + 1.615384615 + x2 = 0 + 1.615384615

Reorder the terms:
-1.615384615 + 1.615384615 + -0.3846153846x + x2 = 0 + 1.615384615

Combine like terms: -1.615384615 + 1.615384615 = 0.000000000
0.000000000 + -0.3846153846x + x2 = 0 + 1.615384615
-0.3846153846x + x2 = 0 + 1.615384615

Combine like terms: 0 + 1.615384615 = 1.615384615
-0.3846153846x + x2 = 1.615384615

The x term is -0.3846153846x.  Take half its coefficient (-0.1923076923).
Square it (0.03698224852) and add it to both sides.

Add '0.03698224852' to each side of the equation.
-0.3846153846x + 0.03698224852 + x2 = 1.615384615 + 0.03698224852

Reorder the terms:
0.03698224852 + -0.3846153846x + x2 = 1.615384615 + 0.03698224852

Combine like terms: 1.615384615 + 0.03698224852 = 1.65236686352
0.03698224852 + -0.3846153846x + x2 = 1.65236686352

Factor a perfect square on the left side:
(x + -0.1923076923)(x + -0.1923076923) = 1.65236686352

Calculate the square root of the right side: 1.285444228

Break this problem into two subproblems by setting 
(x + -0.1923076923) equal to 1.285444228 and -1.285444228.

Subproblem 1

x + -0.1923076923 = 1.285444228 Simplifying x + -0.1923076923 = 1.285444228 Reorder the terms: -0.1923076923 + x = 1.285444228 Solving -0.1923076923 + x = 1.285444228 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1923076923' to each side of the equation. -0.1923076923 + 0.1923076923 + x = 1.285444228 + 0.1923076923 Combine like terms: -0.1923076923 + 0.1923076923 = 0.0000000000 0.0000000000 + x = 1.285444228 + 0.1923076923 x = 1.285444228 + 0.1923076923 Combine like terms: 1.285444228 + 0.1923076923 = 1.4777519203 x = 1.4777519203 Simplifying x = 1.4777519203

Subproblem 2

x + -0.1923076923 = -1.285444228 Simplifying x + -0.1923076923 = -1.285444228 Reorder the terms: -0.1923076923 + x = -1.285444228 Solving -0.1923076923 + x = -1.285444228 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1923076923' to each side of the equation. -0.1923076923 + 0.1923076923 + x = -1.285444228 + 0.1923076923 Combine like terms: -0.1923076923 + 0.1923076923 = 0.0000000000 0.0000000000 + x = -1.285444228 + 0.1923076923 x = -1.285444228 + 0.1923076923 Combine like terms: -1.285444228 + 0.1923076923 = -1.0931365357 x = -1.0931365357 Simplifying x = -1.0931365357

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.4777519203, -1.0931365357}

See similar equations:

| 9(2x-9)=3(6x+1) | | 7+6x=62+x | | 5+4t-4=5t+13-3t | | h(x)=(x-3)2+5 | | -8-16=-8x+5x | | 289-4x=41x+24 | | 7y+y=19-3 | | y(y+12)-8y=14+y(y-4) | | 5z=-2.5 | | x/5=-27 | | 3(4x+1)=-9 | | 7x+2y+6x-5y= | | 5k^2+30k-135=0 | | 3x^3-4x^2-30x=-52 | | 2x-4+6= | | -1n+5(6n+10)=3+36 | | -1n+5(6+10)=3.+36 | | -30-6x=2x+19 | | 10+15-12a=7 | | 5x+12x-4x= | | -5(4b+1)+(21b-6)=0 | | 8(3x-6)=2(12x+3) | | 3.4q-1.4-4.5q=-2.1q-5.4 | | 5+6t-2=9t+15-7t | | 7p+5q-2p+4q= | | 3x^2-6x+3= | | -6k+3(6k-7)=-4-24 | | 8-x=2x+9 | | z^2-7z-30=0 | | x+4.6=4.9 | | 64=y(13+y) | | d^2+3d-28=0 |

Equations solver categories