750+22n(n-12)=650+30(n-10)

Simple and best practice solution for 750+22n(n-12)=650+30(n-10) 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 750+22n(n-12)=650+30(n-10) equation:


Simplifying
750 + 22n(n + -12) = 650 + 30(n + -10)

Reorder the terms:
750 + 22n(-12 + n) = 650 + 30(n + -10)
750 + (-12 * 22n + n * 22n) = 650 + 30(n + -10)
750 + (-264n + 22n2) = 650 + 30(n + -10)

Reorder the terms:
750 + -264n + 22n2 = 650 + 30(-10 + n)
750 + -264n + 22n2 = 650 + (-10 * 30 + n * 30)
750 + -264n + 22n2 = 650 + (-300 + 30n)

Combine like terms: 650 + -300 = 350
750 + -264n + 22n2 = 350 + 30n

Solving
750 + -264n + 22n2 = 350 + 30n

Solving for variable 'n'.

Reorder the terms:
750 + -350 + -264n + -30n + 22n2 = 350 + 30n + -350 + -30n

Combine like terms: 750 + -350 = 400
400 + -264n + -30n + 22n2 = 350 + 30n + -350 + -30n

Combine like terms: -264n + -30n = -294n
400 + -294n + 22n2 = 350 + 30n + -350 + -30n

Reorder the terms:
400 + -294n + 22n2 = 350 + -350 + 30n + -30n

Combine like terms: 350 + -350 = 0
400 + -294n + 22n2 = 0 + 30n + -30n
400 + -294n + 22n2 = 30n + -30n

Combine like terms: 30n + -30n = 0
400 + -294n + 22n2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(200 + -147n + 11n2) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(200 + -147n + 11n2)' equal to zero and attempt to solve: Simplifying 200 + -147n + 11n2 = 0 Solving 200 + -147n + 11n2 = 0 Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. 18.18181818 + -13.36363636n + n2 = 0 Move the constant term to the right: Add '-18.18181818' to each side of the equation. 18.18181818 + -13.36363636n + -18.18181818 + n2 = 0 + -18.18181818 Reorder the terms: 18.18181818 + -18.18181818 + -13.36363636n + n2 = 0 + -18.18181818 Combine like terms: 18.18181818 + -18.18181818 = 0.00000000 0.00000000 + -13.36363636n + n2 = 0 + -18.18181818 -13.36363636n + n2 = 0 + -18.18181818 Combine like terms: 0 + -18.18181818 = -18.18181818 -13.36363636n + n2 = -18.18181818 The n term is -13.36363636n. Take half its coefficient (-6.68181818). Square it (44.64669419) and add it to both sides. Add '44.64669419' to each side of the equation. -13.36363636n + 44.64669419 + n2 = -18.18181818 + 44.64669419 Reorder the terms: 44.64669419 + -13.36363636n + n2 = -18.18181818 + 44.64669419 Combine like terms: -18.18181818 + 44.64669419 = 26.46487601 44.64669419 + -13.36363636n + n2 = 26.46487601 Factor a perfect square on the left side: (n + -6.68181818)(n + -6.68181818) = 26.46487601 Calculate the square root of the right side: 5.144402396 Break this problem into two subproblems by setting (n + -6.68181818) equal to 5.144402396 and -5.144402396.

Subproblem 1

n + -6.68181818 = 5.144402396 Simplifying n + -6.68181818 = 5.144402396 Reorder the terms: -6.68181818 + n = 5.144402396 Solving -6.68181818 + n = 5.144402396 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '6.68181818' to each side of the equation. -6.68181818 + 6.68181818 + n = 5.144402396 + 6.68181818 Combine like terms: -6.68181818 + 6.68181818 = 0.00000000 0.00000000 + n = 5.144402396 + 6.68181818 n = 5.144402396 + 6.68181818 Combine like terms: 5.144402396 + 6.68181818 = 11.826220576 n = 11.826220576 Simplifying n = 11.826220576

Subproblem 2

n + -6.68181818 = -5.144402396 Simplifying n + -6.68181818 = -5.144402396 Reorder the terms: -6.68181818 + n = -5.144402396 Solving -6.68181818 + n = -5.144402396 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '6.68181818' to each side of the equation. -6.68181818 + 6.68181818 + n = -5.144402396 + 6.68181818 Combine like terms: -6.68181818 + 6.68181818 = 0.00000000 0.00000000 + n = -5.144402396 + 6.68181818 n = -5.144402396 + 6.68181818 Combine like terms: -5.144402396 + 6.68181818 = 1.537415784 n = 1.537415784 Simplifying n = 1.537415784

Solution

The solution to the problem is based on the solutions from the subproblems. n = {11.826220576, 1.537415784}

Solution

n = {11.826220576, 1.537415784}

See similar equations:

| 4(X+1)(x-1)= | | 3x+x-5=3x+6 | | 7x^2+23x-4=0 | | (5x-9)-1=(4-3x)(-2)+10 | | 750+22n(n-12)=650+30n(n-10) | | 6+3y-1=5y+14-3y | | 65x=1300 | | 12x^2+7=-12x | | 8+2+8c= | | -4/5(n-6)=12 | | 20=1/5w | | c+cx=b-bx | | (9i)(2i)= | | 0=y-14-2y | | =4s-2(10+5) | | c+cx=b+bx | | 5(d+4)+3(d-2)= | | 21=1/2h(4+3) | | 9x-4(x-5)=3(x-5)+6 | | B+0.375=0.125 | | 120=12(3-2t) | | 1/2(4x-8y) | | 90=78-x | | 3w+8=50 | | 6[4y+5]= | | (2-x)60.5-x=4 | | x-8=.6 | | |10-x/8|4 | | k+8-k+6=3k+4-k | | 4(2x+3)=26-3(x+1) | | 23=5x-4 | | 3x1/4= |

Equations solver categories