6x^2=14x+15

Simple and best practice solution for 6x^2=14x+15 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 6x^2=14x+15 equation:


Simplifying
6x2 = 14x + 15

Reorder the terms:
6x2 = 15 + 14x

Solving
6x2 = 15 + 14x

Solving for variable 'x'.

Reorder the terms:
-15 + -14x + 6x2 = 15 + 14x + -15 + -14x

Reorder the terms:
-15 + -14x + 6x2 = 15 + -15 + 14x + -14x

Combine like terms: 15 + -15 = 0
-15 + -14x + 6x2 = 0 + 14x + -14x
-15 + -14x + 6x2 = 14x + -14x

Combine like terms: 14x + -14x = 0
-15 + -14x + 6x2 = 0

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

Divide each side by '6'.
-2.5 + -2.333333333x + x2 = 0

Move the constant term to the right:

Add '2.5' to each side of the equation.
-2.5 + -2.333333333x + 2.5 + x2 = 0 + 2.5

Reorder the terms:
-2.5 + 2.5 + -2.333333333x + x2 = 0 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + -2.333333333x + x2 = 0 + 2.5
-2.333333333x + x2 = 0 + 2.5

Combine like terms: 0 + 2.5 = 2.5
-2.333333333x + x2 = 2.5

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 = 2.5 + 1.361111112

Reorder the terms:
1.361111112 + -2.333333333x + x2 = 2.5 + 1.361111112

Combine like terms: 2.5 + 1.361111112 = 3.861111112
1.361111112 + -2.333333333x + x2 = 3.861111112

Factor a perfect square on the left side:
(x + -1.166666667)(x + -1.166666667) = 3.861111112

Calculate the square root of the right side: 1.964971021

Break this problem into two subproblems by setting 
(x + -1.166666667) equal to 1.964971021 and -1.964971021.

Subproblem 1

x + -1.166666667 = 1.964971021 Simplifying x + -1.166666667 = 1.964971021 Reorder the terms: -1.166666667 + x = 1.964971021 Solving -1.166666667 + x = 1.964971021 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 = 1.964971021 + 1.166666667 Combine like terms: -1.166666667 + 1.166666667 = 0.000000000 0.000000000 + x = 1.964971021 + 1.166666667 x = 1.964971021 + 1.166666667 Combine like terms: 1.964971021 + 1.166666667 = 3.131637688 x = 3.131637688 Simplifying x = 3.131637688

Subproblem 2

x + -1.166666667 = -1.964971021 Simplifying x + -1.166666667 = -1.964971021 Reorder the terms: -1.166666667 + x = -1.964971021 Solving -1.166666667 + x = -1.964971021 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 = -1.964971021 + 1.166666667 Combine like terms: -1.166666667 + 1.166666667 = 0.000000000 0.000000000 + x = -1.964971021 + 1.166666667 x = -1.964971021 + 1.166666667 Combine like terms: -1.964971021 + 1.166666667 = -0.798304354 x = -0.798304354 Simplifying x = -0.798304354

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.131637688, -0.798304354}

See similar equations:

| 21-15d=35 | | 5x+3=2(x+3) | | 5x^4-3x^2=2 | | r/(-2)+11=15 | | 4x+6=2(x+6) | | -(2x+3)=5 | | 8x=x+7 | | 13x^3+15x^2+21x+7=0 | | 3x-25=2(x-7) | | 16x^2-20z+5=0 | | x^4-2x^3-36x^2=0 | | 4x-4=x+1 | | 16x-20x+5=0 | | d+3/3=d+12/4 | | p=1.50+0.75(t-0.5) | | 4=3x+2 | | x/8+7=118 | | 3=3x+2 | | 1=3x+2 | | 100x-60x-3750000=400000 | | (2x+4)*(6)=192 | | 9000t+900=30 | | 8x+5(5+x)6=2x | | u+90=30 | | 8x+1(x+3)6=2x | | 8x+1(x+3)=2x | | 2c+1.33-4c=-4 | | x+9=6+x | | 4k^2-9k-9=0 | | (k+1)x^2+4kx+9=0 | | 7+1/8(l)=-2 | | -2/5(c)-8=32 |

Equations solver categories