0=-3x^2+7x+8

Simple and best practice solution for 0=-3x^2+7x+8 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 0=-3x^2+7x+8 equation:


Simplifying
0 = -3x2 + 7x + 8

Reorder the terms:
0 = 8 + 7x + -3x2

Solving
0 = 8 + 7x + -3x2

Solving for variable 'x'.

Combine like terms: 0 + -8 = -8
-8 + -7x + 3x2 = 8 + 7x + -3x2 + -8 + -7x + 3x2

Reorder the terms:
-8 + -7x + 3x2 = 8 + -8 + 7x + -7x + -3x2 + 3x2

Combine like terms: 8 + -8 = 0
-8 + -7x + 3x2 = 0 + 7x + -7x + -3x2 + 3x2
-8 + -7x + 3x2 = 7x + -7x + -3x2 + 3x2

Combine like terms: 7x + -7x = 0
-8 + -7x + 3x2 = 0 + -3x2 + 3x2
-8 + -7x + 3x2 = -3x2 + 3x2

Combine like terms: -3x2 + 3x2 = 0
-8 + -7x + 3x2 = 0

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

Divide each side by '3'.
-2.666666667 + -2.333333333x + x2 = 0

Move the constant term to the right:

Add '2.666666667' to each side of the equation.
-2.666666667 + -2.333333333x + 2.666666667 + x2 = 0 + 2.666666667

Reorder the terms:
-2.666666667 + 2.666666667 + -2.333333333x + x2 = 0 + 2.666666667

Combine like terms: -2.666666667 + 2.666666667 = 0.000000000
0.000000000 + -2.333333333x + x2 = 0 + 2.666666667
-2.333333333x + x2 = 0 + 2.666666667

Combine like terms: 0 + 2.666666667 = 2.666666667
-2.333333333x + x2 = 2.666666667

The x term is -2.333333333x.  Take half its coefficient (-1.166666667).
Square it (1.361111112) and add it to both sides.

Add '1.361111112' to each side of the equation.
-2.333333333x + 1.361111112 + x2 = 2.666666667 + 1.361111112

Reorder the terms:
1.361111112 + -2.333333333x + x2 = 2.666666667 + 1.361111112

Combine like terms: 2.666666667 + 1.361111112 = 4.027777779
1.361111112 + -2.333333333x + x2 = 4.027777779

Factor a perfect square on the left side:
(x + -1.166666667)(x + -1.166666667) = 4.027777779

Calculate the square root of the right side: 2.00693243

Break this problem into two subproblems by setting 
(x + -1.166666667) equal to 2.00693243 and -2.00693243.

Subproblem 1

x + -1.166666667 = 2.00693243 Simplifying x + -1.166666667 = 2.00693243 Reorder the terms: -1.166666667 + x = 2.00693243 Solving -1.166666667 + x = 2.00693243 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.166666667' to each side of the equation. -1.166666667 + 1.166666667 + x = 2.00693243 + 1.166666667 Combine like terms: -1.166666667 + 1.166666667 = 0.000000000 0.000000000 + x = 2.00693243 + 1.166666667 x = 2.00693243 + 1.166666667 Combine like terms: 2.00693243 + 1.166666667 = 3.173599097 x = 3.173599097 Simplifying x = 3.173599097

Subproblem 2

x + -1.166666667 = -2.00693243 Simplifying x + -1.166666667 = -2.00693243 Reorder the terms: -1.166666667 + x = -2.00693243 Solving -1.166666667 + x = -2.00693243 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.166666667' to each side of the equation. -1.166666667 + 1.166666667 + x = -2.00693243 + 1.166666667 Combine like terms: -1.166666667 + 1.166666667 = 0.000000000 0.000000000 + x = -2.00693243 + 1.166666667 x = -2.00693243 + 1.166666667 Combine like terms: -2.00693243 + 1.166666667 = -0.840265763 x = -0.840265763 Simplifying x = -0.840265763

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.173599097, -0.840265763}

See similar equations:

| 3X+1+5=11 | | 0=-8x^2+5x+3 | | f(x)=79 | | y=(10)+7 | | (42x-9)=(35x+12) | | .2n-12=-8 | | (26x-7)=(20x+17) | | 0=-3x^2+6x+3 | | x+(y+7)=17 | | f(x)=-3x^2+6x+3 | | (-2)+y=8 | | 0=-5x^2+6x+5 | | 8t^2+38t-10=0 | | 4.2E=-21 | | 4(y-4)+7= | | g(.5)+g=352 | | 10x^2+12x-16=0 | | 3X-6=78 | | 70x^2+63x+14=0 | | 4.75+e=-3.1 | | (6-y)(4y-9)=0 | | 112+3k=112 | | (-2x+3)(5x+7)=0 | | 225+2g+2g+g=1020 | | (225+2g)+g=1020 | | -4=2x-y | | z^2+z-30=0 | | (5r-2y)-(2r-3y)= | | 28.25+0.18m=19.85+0.32m | | f=-.50+a*2 | | 4x=x^2-9 | | -.50+250*2= |

Equations solver categories