7x^2+15x=205

Simple and best practice solution for 7x^2+15x=205 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 7x^2+15x=205 equation:


Simplifying
7x2 + 15x = 205

Reorder the terms:
15x + 7x2 = 205

Solving
15x + 7x2 = 205

Solving for variable 'x'.

Reorder the terms:
-205 + 15x + 7x2 = 205 + -205

Combine like terms: 205 + -205 = 0
-205 + 15x + 7x2 = 0

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

Divide each side by '7'.
-29.28571429 + 2.142857143x + x2 = 0

Move the constant term to the right:

Add '29.28571429' to each side of the equation.
-29.28571429 + 2.142857143x + 29.28571429 + x2 = 0 + 29.28571429

Reorder the terms:
-29.28571429 + 29.28571429 + 2.142857143x + x2 = 0 + 29.28571429

Combine like terms: -29.28571429 + 29.28571429 = 0.00000000
0.00000000 + 2.142857143x + x2 = 0 + 29.28571429
2.142857143x + x2 = 0 + 29.28571429

Combine like terms: 0 + 29.28571429 = 29.28571429
2.142857143x + x2 = 29.28571429

The x term is 2.142857143x.  Take half its coefficient (1.071428572).
Square it (1.147959185) and add it to both sides.

Add '1.147959185' to each side of the equation.
2.142857143x + 1.147959185 + x2 = 29.28571429 + 1.147959185

Reorder the terms:
1.147959185 + 2.142857143x + x2 = 29.28571429 + 1.147959185

Combine like terms: 29.28571429 + 1.147959185 = 30.433673475
1.147959185 + 2.142857143x + x2 = 30.433673475

Factor a perfect square on the left side:
(x + 1.071428572)(x + 1.071428572) = 30.433673475

Calculate the square root of the right side: 5.516672319

Break this problem into two subproblems by setting 
(x + 1.071428572) equal to 5.516672319 and -5.516672319.

Subproblem 1

x + 1.071428572 = 5.516672319 Simplifying x + 1.071428572 = 5.516672319 Reorder the terms: 1.071428572 + x = 5.516672319 Solving 1.071428572 + x = 5.516672319 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.071428572' to each side of the equation. 1.071428572 + -1.071428572 + x = 5.516672319 + -1.071428572 Combine like terms: 1.071428572 + -1.071428572 = 0.000000000 0.000000000 + x = 5.516672319 + -1.071428572 x = 5.516672319 + -1.071428572 Combine like terms: 5.516672319 + -1.071428572 = 4.445243747 x = 4.445243747 Simplifying x = 4.445243747

Subproblem 2

x + 1.071428572 = -5.516672319 Simplifying x + 1.071428572 = -5.516672319 Reorder the terms: 1.071428572 + x = -5.516672319 Solving 1.071428572 + x = -5.516672319 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.071428572' to each side of the equation. 1.071428572 + -1.071428572 + x = -5.516672319 + -1.071428572 Combine like terms: 1.071428572 + -1.071428572 = 0.000000000 0.000000000 + x = -5.516672319 + -1.071428572 x = -5.516672319 + -1.071428572 Combine like terms: -5.516672319 + -1.071428572 = -6.588100891 x = -6.588100891 Simplifying x = -6.588100891

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4.445243747, -6.588100891}

See similar equations:

| 2(x+4)-5y= | | x+2x+(x+76)=180 | | -9f=57 | | 6n+n=56 | | 39.97=8g+3.73 | | 4w^2+12w-160=0 | | -2(w-2)+4w+3= | | 4x-6=4x+2 | | 6x+4x-7=33 | | 2x-4=x-16 | | 1.68g-10=0.92 | | 14=-2y-3 | | 8x=x-8 | | 7x^2-2b^2-1=0 | | 12-(x+1)=3+x | | 4.4+10m=8.76 | | -3+3=6 | | 9y-13y=24 | | r-[-6]=8 | | 0.2+0.1=X-2 | | -2(6n+3)=-102 | | 2A^2-A-A-13=2 | | -4(x-2)=5x-10 | | -2(y-4)-2y=8 | | -244=-4(7k+5) | | 7(2c-5)-7= | | v^3+5=32 | | 2(n+4)-3n+m= | | 2x+3x=12-2 | | 10r-6r= | | 8X+60=9X | | -13=2M+1-6 |

Equations solver categories