2x^2+14x=15

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


Simplifying
2x2 + 14x = 15

Reorder the terms:
14x + 2x2 = 15

Solving
14x + 2x2 = 15

Solving for variable 'x'.

Reorder the terms:
-15 + 14x + 2x2 = 15 + -15

Combine like terms: 15 + -15 = 0
-15 + 14x + 2x2 = 0

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

Divide each side by '2'.
-7.5 + 7x + x2 = 0

Move the constant term to the right:

Add '7.5' to each side of the equation.
-7.5 + 7x + 7.5 + x2 = 0 + 7.5

Reorder the terms:
-7.5 + 7.5 + 7x + x2 = 0 + 7.5

Combine like terms: -7.5 + 7.5 = 0.0
0.0 + 7x + x2 = 0 + 7.5
7x + x2 = 0 + 7.5

Combine like terms: 0 + 7.5 = 7.5
7x + x2 = 7.5

The x term is 7x.  Take half its coefficient (3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
7x + 12.25 + x2 = 7.5 + 12.25

Reorder the terms:
12.25 + 7x + x2 = 7.5 + 12.25

Combine like terms: 7.5 + 12.25 = 19.75
12.25 + 7x + x2 = 19.75

Factor a perfect square on the left side:
(x + 3.5)(x + 3.5) = 19.75

Calculate the square root of the right side: 4.444097209

Break this problem into two subproblems by setting 
(x + 3.5) equal to 4.444097209 and -4.444097209.

Subproblem 1

x + 3.5 = 4.444097209 Simplifying x + 3.5 = 4.444097209 Reorder the terms: 3.5 + x = 4.444097209 Solving 3.5 + x = 4.444097209 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = 4.444097209 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 4.444097209 + -3.5 x = 4.444097209 + -3.5 Combine like terms: 4.444097209 + -3.5 = 0.944097209 x = 0.944097209 Simplifying x = 0.944097209

Subproblem 2

x + 3.5 = -4.444097209 Simplifying x + 3.5 = -4.444097209 Reorder the terms: 3.5 + x = -4.444097209 Solving 3.5 + x = -4.444097209 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = -4.444097209 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -4.444097209 + -3.5 x = -4.444097209 + -3.5 Combine like terms: -4.444097209 + -3.5 = -7.944097209 x = -7.944097209 Simplifying x = -7.944097209

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.944097209, -7.944097209}

See similar equations:

| 13z-2=30z-2 | | 8x+9y=24fory | | -2x-10=8x+10 | | 4.95L=G | | 2(8w+9)= | | 13+7x=9x+1 | | 4(3x-5)-x=-c+16 | | -9(e+8)=45 | | 13.5^(2/3) | | 3x+2x-20=13 | | -8a+7=1-7a | | 2.5x+11=35 | | 12x^2-37x+3=0 | | =15n+85 | | -16x^2+176x-480=0 | | 75x^3y-65x^2y+10xy=0 | | 3G-35=-62 | | 3x^5+2x^3-5=0 | | 2x-7/13=2x-3/9 | | -8-8=-24 | | 5x^2-20x-44=0 | | 6x+10+6x-10=180 | | 11y+15=180 | | 8-7i= | | 25a-12/8=4 | | -3(4s-5)-15=-2(8s+2)-2 | | (3/7)^3 | | 126=6-4x | | 8=-8y+6(y+2) | | 75x^3y-65x^2+10xy=0 | | 7(18-x)-6(3-5x)=-(7x+9)-3(2x+5)+24 | | 8v^2-32w^2=0 |

Equations solver categories