7p^2+7p-18=0

Simple and best practice solution for 7p^2+7p-18=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 7p^2+7p-18=0 equation:


Simplifying
7p2 + 7p + -18 = 0

Reorder the terms:
-18 + 7p + 7p2 = 0

Solving
-18 + 7p + 7p2 = 0

Solving for variable 'p'.

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

Divide each side by '7'.
-2.571428571 + p + p2 = 0

Move the constant term to the right:

Add '2.571428571' to each side of the equation.
-2.571428571 + p + 2.571428571 + p2 = 0 + 2.571428571

Reorder the terms:
-2.571428571 + 2.571428571 + p + p2 = 0 + 2.571428571

Combine like terms: -2.571428571 + 2.571428571 = 0.000000000
0.000000000 + p + p2 = 0 + 2.571428571
p + p2 = 0 + 2.571428571

Combine like terms: 0 + 2.571428571 = 2.571428571
p + p2 = 2.571428571

The p term is p.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
 + 0.25 + p2 = 2.571428571 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + p2 = 2.571428571 + 0.25

Combine like terms: 2.571428571 + 0.25 = 2.821428571
1.25 + p2 = 2.821428571

Factor a perfect square on the left side:
(p + 0.5)(p + 0.5) = 2.821428571

Calculate the square root of the right side: 1.679710859

Break this problem into two subproblems by setting 
(p + 0.5) equal to 1.679710859 and -1.679710859.

Subproblem 1

p + 0.5 = 1.679710859 Simplifying p + 0.5 = 1.679710859 Reorder the terms: 0.5 + p = 1.679710859 Solving 0.5 + p = 1.679710859 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + p = 1.679710859 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + p = 1.679710859 + -0.5 p = 1.679710859 + -0.5 Combine like terms: 1.679710859 + -0.5 = 1.179710859 p = 1.179710859 Simplifying p = 1.179710859

Subproblem 2

p + 0.5 = -1.679710859 Simplifying p + 0.5 = -1.679710859 Reorder the terms: 0.5 + p = -1.679710859 Solving 0.5 + p = -1.679710859 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + p = -1.679710859 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + p = -1.679710859 + -0.5 p = -1.679710859 + -0.5 Combine like terms: -1.679710859 + -0.5 = -2.179710859 p = -2.179710859 Simplifying p = -2.179710859

Solution

The solution to the problem is based on the solutions from the subproblems. p = {1.179710859, -2.179710859}

See similar equations:

| 3(5m-1)-2=4(3m-2)+6 | | 6(n+7)+2=9n+38-5n | | 17p+3-6p^2=0 | | 3sinx-9cosx=0 | | 6y-3=21-6y | | 12x+9=3x(4+3) | | 5(4m-3)-8=37 | | 3x(5+3x)=9 | | 2(2x-5)+5x=2x-3(x+2) | | 4x^3+12x^2-19x-12=0 | | 8w-3w+6=-34 | | 15x=-17 | | R(r+8.7)=721.3 | | 4x^2-40x+55=0 | | 4x^3+16x^2-3x-12=0 | | x^2y+x^3-6xy^2=0 | | x^2-6x-4=6 | | 7x+3*0=-16 | | 4b+8=10b-18 | | t^2=6t+43 | | 4b=10b-8 | | -3mn+m^2+2n^2=0 | | 2w^2+w=12 | | c^2+7cd-18d^2=0 | | w=48+(4/7)w | | 10-2q=1.5q+1 | | =(x+9)(9x+1) | | 3.2x=22.2 | | 6x+y^2=42 | | f(x)=50/x^2-25 | | 3x^2y+27xy-87y=0 | | 4[X+7]=80 |

Equations solver categories