x(x+7)=84

Simple and best practice solution for x(x+7)=84 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 x(x+7)=84 equation:


Simplifying
x(x + 7) = 84

Reorder the terms:
x(7 + x) = 84
(7 * x + x * x) = 84
(7x + x2) = 84

Solving
7x + x2 = 84

Solving for variable 'x'.

Reorder the terms:
-84 + 7x + x2 = 84 + -84

Combine like terms: 84 + -84 = 0
-84 + 7x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '84' to each side of the equation.
-84 + 7x + 84 + x2 = 0 + 84

Reorder the terms:
-84 + 84 + 7x + x2 = 0 + 84

Combine like terms: -84 + 84 = 0
0 + 7x + x2 = 0 + 84
7x + x2 = 0 + 84

Combine like terms: 0 + 84 = 84
7x + x2 = 84

The x term is 7x.  Take half its coefficient (3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
7x + 12.25 + x2 = 84 + 12.25

Reorder the terms:
12.25 + 7x + x2 = 84 + 12.25

Combine like terms: 84 + 12.25 = 96.25
12.25 + 7x + x2 = 96.25

Factor a perfect square on the left side:
(x + 3.5)(x + 3.5) = 96.25

Calculate the square root of the right side: 9.810708435

Break this problem into two subproblems by setting 
(x + 3.5) equal to 9.810708435 and -9.810708435.

Subproblem 1

x + 3.5 = 9.810708435 Simplifying x + 3.5 = 9.810708435 Reorder the terms: 3.5 + x = 9.810708435 Solving 3.5 + x = 9.810708435 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = 9.810708435 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 9.810708435 + -3.5 x = 9.810708435 + -3.5 Combine like terms: 9.810708435 + -3.5 = 6.310708435 x = 6.310708435 Simplifying x = 6.310708435

Subproblem 2

x + 3.5 = -9.810708435 Simplifying x + 3.5 = -9.810708435 Reorder the terms: 3.5 + x = -9.810708435 Solving 3.5 + x = -9.810708435 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = -9.810708435 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -9.810708435 + -3.5 x = -9.810708435 + -3.5 Combine like terms: -9.810708435 + -3.5 = -13.310708435 x = -13.310708435 Simplifying x = -13.310708435

Solution

The solution to the problem is based on the solutions from the subproblems. x = {6.310708435, -13.310708435}

See similar equations:

| 4.75+x+x=2+x+x+3.50 | | 5k+14=3k-7 | | 5/6÷8= | | 45*x-6=50*x-6 | | 2*(3x+3)=18 | | 45x-6=50x-6 | | 5(14-39/3)+4*.25= | | 2(f+6)-2=3f-5 | | x^3-x^2-4x+4=y | | 25(x+3)=5(x-1) | | 4u+11=47 | | 1600=3t^2+60t | | 1.20+x+x=5.00 | | (X+3).75=1.6 | | 1.6(t-6)=0.4 | | 4=2x+2y | | (d+3)2.5=30 | | 4/7×2/7 | | 2-3=100 | | 5m^2-2m-2=0 | | -7(2x-6)+5=-14x+47 | | -(4+4y)+4y=4 | | 3x-2x=24-2x | | 2x+3y=235 | | Y=X^2+bx-36 | | -(-3+3y)+3y=3 | | 1.20+2*=5.00 | | 15x-(24)=2x | | N-24=-3n | | 7*y-3=-8 | | 5*n-1/4=-1 | | 8px+16qy-3qx-16py= |

Equations solver categories