3x^2+5x+13=16

Simple and best practice solution for 3x^2+5x+13=16 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+13=16 equation:


Simplifying
3x2 + 5x + 13 = 16

Reorder the terms:
13 + 5x + 3x2 = 16

Solving
13 + 5x + 3x2 = 16

Solving for variable 'x'.

Reorder the terms:
13 + -16 + 5x + 3x2 = 16 + -16

Combine like terms: 13 + -16 = -3
-3 + 5x + 3x2 = 16 + -16

Combine like terms: 16 + -16 = 0
-3 + 5x + 3x2 = 0

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

Divide each side by '3'.
-1 + 1.666666667x + x2 = 0

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + 1.666666667x + 1 + x2 = 0 + 1

Reorder the terms:
-1 + 1 + 1.666666667x + x2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 1.666666667x + x2 = 0 + 1
1.666666667x + x2 = 0 + 1

Combine like terms: 0 + 1 = 1
1.666666667x + x2 = 1

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 = 1 + 0.6944444447

Reorder the terms:
0.6944444447 + 1.666666667x + x2 = 1 + 0.6944444447

Combine like terms: 1 + 0.6944444447 = 1.6944444447
0.6944444447 + 1.666666667x + x2 = 1.6944444447

Factor a perfect square on the left side:
(x + 0.8333333335)(x + 0.8333333335) = 1.6944444447

Calculate the square root of the right side: 1.301708279

Break this problem into two subproblems by setting 
(x + 0.8333333335) equal to 1.301708279 and -1.301708279.

Subproblem 1

x + 0.8333333335 = 1.301708279 Simplifying x + 0.8333333335 = 1.301708279 Reorder the terms: 0.8333333335 + x = 1.301708279 Solving 0.8333333335 + x = 1.301708279 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 = 1.301708279 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + x = 1.301708279 + -0.8333333335 x = 1.301708279 + -0.8333333335 Combine like terms: 1.301708279 + -0.8333333335 = 0.4683749455 x = 0.4683749455 Simplifying x = 0.4683749455

Subproblem 2

x + 0.8333333335 = -1.301708279 Simplifying x + 0.8333333335 = -1.301708279 Reorder the terms: 0.8333333335 + x = -1.301708279 Solving 0.8333333335 + x = -1.301708279 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 = -1.301708279 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + x = -1.301708279 + -0.8333333335 x = -1.301708279 + -0.8333333335 Combine like terms: -1.301708279 + -0.8333333335 = -2.1350416125 x = -2.1350416125 Simplifying x = -2.1350416125

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.4683749455, -2.1350416125}

See similar equations:

| -7p-9=b-113 | | 7*20= | | 7-4(7-3)=23 | | -8x-40=2x | | -4x+5+9x-2andx=6 | | 2x+3(x-7)=-1 | | m=n+2p | | 5p-6=p+106 | | 5x+23=-2 | | 5b-4b=-2 | | 1x+8+4=17 | | -28.3y-82.3=y+1083.84 | | -4.3x=-10.75 | | -3(x+4)+2x=2(x-6)-3x | | 4x+17=-7 | | 2.4(1.3)x=9.6 | | 5c-2e+1=15 | | 13.5r+7.5=r-590 | | 3+(x-2)= | | 4(x+4)=2x+20 | | -3y+11+2x-y=1 | | x-(-22)=-6 | | -8.2p+7.2=p+267.56 | | -7x+3=-19 | | -3c+4=c+96 | | (24ab)(3)= | | a-17.72=1.6a+4 | | 5x-2c+1=15 | | 24overx=-10 | | -8x^3+5x^2-20x+250=0 | | -8q+8=q+311.3 | | 7.2=-3h |

Equations solver categories