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 = 0.840265763 x = 0.840265763 Simplifying x = 0.840265763

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 = -3.173599097 x = -3.173599097 Simplifying x = -3.173599097

Solution

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

See similar equations:

| 6(2a-3)=7 | | 77=3m-14 | | X^2+13x-1=0 | | 0=2x^2-2x+5 | | -13-2x=2+3x | | 2+2w=0 | | 0=(x^2+16)(x^2-25) | | 13cm+5cm=b | | y=(x^2+16)(x^2-25) | | -21.6=5.4v | | x/2-12=15 | | f(x)=(x^2+16)(x^2-25) | | 8c-86=72 | | 6(x-10)=-18 | | x(3)=2(x+5) | | -9=-4+c | | 6(x-109)=-6 | | 8ft+6ft=c | | 10=100000000 | | -6(w+3)-(-8w-4)=w | | 6(x-3)-8(x+2)=5-3(x-4) | | N/6-2=1 | | -6n-20=-2n+4(1-13n) | | 3x+2=5x+w | | 3x^2-24x+7=0 | | 14=7x/10=8 | | 0=x^2+10x+33 | | 3(x+3)=2x-9 | | 78=6b | | x^2=4x^2-36x+81 | | X+52=x+47 | | 4(3+x)-x=6(x+2) |

Equations solver categories