120=10x+4.9x^2

Simple and best practice solution for 120=10x+4.9x^2 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 120=10x+4.9x^2 equation:


Simplifying
120 = 10x + 4.9x2

Solving
120 = 10x + 4.9x2

Solving for variable 'x'.

Reorder the terms:
120 + -10x + -4.9x2 = 10x + -10x + 4.9x2 + -4.9x2

Combine like terms: 10x + -10x = 0
120 + -10x + -4.9x2 = 0 + 4.9x2 + -4.9x2
120 + -10x + -4.9x2 = 4.9x2 + -4.9x2

Combine like terms: 4.9x2 + -4.9x2 = 0.0
120 + -10x + -4.9x2 = 0.0

Begin completing the square.  Divide all terms by
-4.9 the coefficient of the squared term: 

Divide each side by '-4.9'.
-24.48979592 + 2.040816327x + x2 = 0

Move the constant term to the right:

Add '24.48979592' to each side of the equation.
-24.48979592 + 2.040816327x + 24.48979592 + x2 = 0 + 24.48979592

Reorder the terms:
-24.48979592 + 24.48979592 + 2.040816327x + x2 = 0 + 24.48979592

Combine like terms: -24.48979592 + 24.48979592 = 0.00000000
0.00000000 + 2.040816327x + x2 = 0 + 24.48979592
2.040816327x + x2 = 0 + 24.48979592

Combine like terms: 0 + 24.48979592 = 24.48979592
2.040816327x + x2 = 24.48979592

The x term is 2.040816327x.  Take half its coefficient (1.020408164).
Square it (1.041232821) and add it to both sides.

Add '1.041232821' to each side of the equation.
2.040816327x + 1.041232821 + x2 = 24.48979592 + 1.041232821

Reorder the terms:
1.041232821 + 2.040816327x + x2 = 24.48979592 + 1.041232821

Combine like terms: 24.48979592 + 1.041232821 = 25.531028741
1.041232821 + 2.040816327x + x2 = 25.531028741

Factor a perfect square on the left side:
(x + 1.020408164)(x + 1.020408164) = 25.531028741

Calculate the square root of the right side: 5.052823838

Break this problem into two subproblems by setting 
(x + 1.020408164) equal to 5.052823838 and -5.052823838.

Subproblem 1

x + 1.020408164 = 5.052823838 Simplifying x + 1.020408164 = 5.052823838 Reorder the terms: 1.020408164 + x = 5.052823838 Solving 1.020408164 + x = 5.052823838 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.020408164' to each side of the equation. 1.020408164 + -1.020408164 + x = 5.052823838 + -1.020408164 Combine like terms: 1.020408164 + -1.020408164 = 0.000000000 0.000000000 + x = 5.052823838 + -1.020408164 x = 5.052823838 + -1.020408164 Combine like terms: 5.052823838 + -1.020408164 = 4.032415674 x = 4.032415674 Simplifying x = 4.032415674

Subproblem 2

x + 1.020408164 = -5.052823838 Simplifying x + 1.020408164 = -5.052823838 Reorder the terms: 1.020408164 + x = -5.052823838 Solving 1.020408164 + x = -5.052823838 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.020408164' to each side of the equation. 1.020408164 + -1.020408164 + x = -5.052823838 + -1.020408164 Combine like terms: 1.020408164 + -1.020408164 = 0.000000000 0.000000000 + x = -5.052823838 + -1.020408164 x = -5.052823838 + -1.020408164 Combine like terms: -5.052823838 + -1.020408164 = -6.073232002 x = -6.073232002 Simplifying x = -6.073232002

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4.032415674, -6.073232002}

See similar equations:

| v/3=45 | | 45x=70(x+3.5) | | 0.04x=20000 | | (2x+1)2-2(x-5)+6=3(x+1)+(x-1)2+23 | | 40+5x=120 | | (7+z)(4z-6)=0 | | 9y+8=8 | | -3(d-3)=12 | | 0.04x=50000 | | 7=3-n+3 | | 0n+1-4n=-3 | | 2(3p-10)=40 | | 0.6x+0.5=0.3 | | (1-y^2)dx=xdy | | Z^4-2z^3+2z^2-2z+1=0 | | 2-3n-1n=2 | | 5x-2/3y=-12 | | 75x+3120=8250 | | 3=3-3n+2n | | y=64+5 | | 15/20=21/x | | 68+56+52+58+68+72+71+64+68+77+66+55+68+71= | | 2.2x-5.76=4.1-0.7x | | (x+1)2+2(x-3)-5=(x+2)2-(x+3)+2 | | 0n-4n-1=-1 | | 28=x+20 | | 2x+8+3x+5= | | 0n-2n+3=-1 | | 2.2x-5.76=4.1-0.4x | | 28+4x=15 | | y/2-13=19 | | 3x-(2x-6)=6 |

Equations solver categories