3x^2+5x=10

Simple and best practice solution for 3x^2+5x=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 3x^2+5x=10 equation:


Simplifying
3x2 + 5x = 10

Reorder the terms:
5x + 3x2 = 10

Solving
5x + 3x2 = 10

Solving for variable 'x'.

Reorder the terms:
-10 + 5x + 3x2 = 10 + -10

Combine like terms: 10 + -10 = 0
-10 + 5x + 3x2 = 0

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

Divide each side by '3'.
-3.333333333 + 1.666666667x + x2 = 0

Move the constant term to the right:

Add '3.333333333' to each side of the equation.
-3.333333333 + 1.666666667x + 3.333333333 + x2 = 0 + 3.333333333

Reorder the terms:
-3.333333333 + 3.333333333 + 1.666666667x + x2 = 0 + 3.333333333

Combine like terms: -3.333333333 + 3.333333333 = 0.000000000
0.000000000 + 1.666666667x + x2 = 0 + 3.333333333
1.666666667x + x2 = 0 + 3.333333333

Combine like terms: 0 + 3.333333333 = 3.333333333
1.666666667x + x2 = 3.333333333

The x term is 1.666666667x.  Take half its coefficient (0.8333333335).
Square it (0.6944444447) and add it to both sides.

Add '0.6944444447' to each side of the equation.
1.666666667x + 0.6944444447 + x2 = 3.333333333 + 0.6944444447

Reorder the terms:
0.6944444447 + 1.666666667x + x2 = 3.333333333 + 0.6944444447

Combine like terms: 3.333333333 + 0.6944444447 = 4.0277777777
0.6944444447 + 1.666666667x + x2 = 4.0277777777

Factor a perfect square on the left side:
(x + 0.8333333335)(x + 0.8333333335) = 4.0277777777

Calculate the square root of the right side: 2.00693243

Break this problem into two subproblems by setting 
(x + 0.8333333335) equal to 2.00693243 and -2.00693243.

Subproblem 1

x + 0.8333333335 = 2.00693243 Simplifying x + 0.8333333335 = 2.00693243 Reorder the terms: 0.8333333335 + x = 2.00693243 Solving 0.8333333335 + x = 2.00693243 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8333333335' to each side of the equation. 0.8333333335 + -0.8333333335 + x = 2.00693243 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + x = 2.00693243 + -0.8333333335 x = 2.00693243 + -0.8333333335 Combine like terms: 2.00693243 + -0.8333333335 = 1.1735990965 x = 1.1735990965 Simplifying x = 1.1735990965

Subproblem 2

x + 0.8333333335 = -2.00693243 Simplifying x + 0.8333333335 = -2.00693243 Reorder the terms: 0.8333333335 + x = -2.00693243 Solving 0.8333333335 + x = -2.00693243 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8333333335' to each side of the equation. 0.8333333335 + -0.8333333335 + x = -2.00693243 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + x = -2.00693243 + -0.8333333335 x = -2.00693243 + -0.8333333335 Combine like terms: -2.00693243 + -0.8333333335 = -2.8402657635 x = -2.8402657635 Simplifying x = -2.8402657635

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.1735990965, -2.8402657635}

See similar equations:

| 7p-2=-11+4p | | Ln(2x-8)=3 | | p(y)=8y-12y-5 | | 3x+5=-4+6x | | -(3y+3)-(-2y-8)=2 | | 7+6x=4x+13 | | 26.9+h=12.74 | | 8(n+8)=3(5n-2) | | 7=x^2+x+1 | | 6(4x-1)=2(12x+5) | | 28=(x+6)(x-6) | | 10n-1=-2n-13 | | 5+12r-2=9r+63-7r | | h+3/6=-4 | | -2x+12y=15 | | 3x^2+12x+37=0 | | x+4+3x=44 | | -8(-5b+7)+5b=0 | | 39.99+0.45r=62.49 | | 4h-16=12 | | 0=4m | | 6x-9=7x+7 | | -y^4+3y^2+18=0 | | 7(x-6)=7 | | 81x^2-45x-36=0 | | 3(a+2)-7=13-(a-2) | | 8x+6y=0 | | 2(10x+12)=4 | | 23x-45+-38x=-15 | | 5(x-2)+12=3 | | 5m-2(m+2)=2m+15 | | 9s-23=-9+7s |

Equations solver categories