2x^2+5x=13

Simple and best practice solution for 2x^2+5x=13 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 2x^2+5x=13 equation:


Simplifying
2x2 + 5x = 13

Reorder the terms:
5x + 2x2 = 13

Solving
5x + 2x2 = 13

Solving for variable 'x'.

Reorder the terms:
-13 + 5x + 2x2 = 13 + -13

Combine like terms: 13 + -13 = 0
-13 + 5x + 2x2 = 0

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

Divide each side by '2'.
-6.5 + 2.5x + x2 = 0

Move the constant term to the right:

Add '6.5' to each side of the equation.
-6.5 + 2.5x + 6.5 + x2 = 0 + 6.5

Reorder the terms:
-6.5 + 6.5 + 2.5x + x2 = 0 + 6.5

Combine like terms: -6.5 + 6.5 = 0.0
0.0 + 2.5x + x2 = 0 + 6.5
2.5x + x2 = 0 + 6.5

Combine like terms: 0 + 6.5 = 6.5
2.5x + x2 = 6.5

The x term is 2.5x.  Take half its coefficient (1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
2.5x + 1.5625 + x2 = 6.5 + 1.5625

Reorder the terms:
1.5625 + 2.5x + x2 = 6.5 + 1.5625

Combine like terms: 6.5 + 1.5625 = 8.0625
1.5625 + 2.5x + x2 = 8.0625

Factor a perfect square on the left side:
(x + 1.25)(x + 1.25) = 8.0625

Calculate the square root of the right side: 2.839454173

Break this problem into two subproblems by setting 
(x + 1.25) equal to 2.839454173 and -2.839454173.

Subproblem 1

x + 1.25 = 2.839454173 Simplifying x + 1.25 = 2.839454173 Reorder the terms: 1.25 + x = 2.839454173 Solving 1.25 + x = 2.839454173 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = 2.839454173 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = 2.839454173 + -1.25 x = 2.839454173 + -1.25 Combine like terms: 2.839454173 + -1.25 = 1.589454173 x = 1.589454173 Simplifying x = 1.589454173

Subproblem 2

x + 1.25 = -2.839454173 Simplifying x + 1.25 = -2.839454173 Reorder the terms: 1.25 + x = -2.839454173 Solving 1.25 + x = -2.839454173 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = -2.839454173 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = -2.839454173 + -1.25 x = -2.839454173 + -1.25 Combine like terms: -2.839454173 + -1.25 = -4.089454173 x = -4.089454173 Simplifying x = -4.089454173

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.589454173, -4.089454173}

See similar equations:

| 22-h=17 | | 59=19+4b | | -24x^5+80x^4+80x^3+6x-12=0 | | -2=15d+43 | | -5(y-2)+9=-11 | | 0.2x^3-24x=0 | | 9m-27=27 | | 6sinx=cosx | | -4m+29=-7 | | 19+5v=64 | | (9x^2+6x+8)=0 | | 96/112 | | 30+x+60-x+2x=90 | | Z+25+Z-15=90 | | x^2-10x-21= | | 5x=9+3 | | -6m=105 | | (8x-9)-(10x^2+x-3)= | | 11x+22=66 | | (x+2)2=8 | | 0=-16x^2+24 | | (7x+5)(5x-4)=0 | | 2a-3b=-3 | | 8/12-3/13 | | -5=q/18 | | -3a+b=-2 | | 4x-2(x-5)=-9+5x+13 | | (5n^(2n))^(1/n) | | 8r=3-16 | | -2z^2+162=0 | | sqrt-4=x | | 10x-6x+192=10x+84 |

Equations solver categories