7x^2-6x-23=0

Simple and best practice solution for 7x^2-6x-23=0 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 7x^2-6x-23=0 equation:


Simplifying
7x2 + -6x + -23 = 0

Reorder the terms:
-23 + -6x + 7x2 = 0

Solving
-23 + -6x + 7x2 = 0

Solving for variable 'x'.

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

Divide each side by '7'.
-3.285714286 + -0.8571428571x + x2 = 0

Move the constant term to the right:

Add '3.285714286' to each side of the equation.
-3.285714286 + -0.8571428571x + 3.285714286 + x2 = 0 + 3.285714286

Reorder the terms:
-3.285714286 + 3.285714286 + -0.8571428571x + x2 = 0 + 3.285714286

Combine like terms: -3.285714286 + 3.285714286 = 0.000000000
0.000000000 + -0.8571428571x + x2 = 0 + 3.285714286
-0.8571428571x + x2 = 0 + 3.285714286

Combine like terms: 0 + 3.285714286 = 3.285714286
-0.8571428571x + x2 = 3.285714286

The x term is -0.8571428571x.  Take half its coefficient (-0.4285714286).
Square it (0.1836734694) and add it to both sides.

Add '0.1836734694' to each side of the equation.
-0.8571428571x + 0.1836734694 + x2 = 3.285714286 + 0.1836734694

Reorder the terms:
0.1836734694 + -0.8571428571x + x2 = 3.285714286 + 0.1836734694

Combine like terms: 3.285714286 + 0.1836734694 = 3.4693877554
0.1836734694 + -0.8571428571x + x2 = 3.4693877554

Factor a perfect square on the left side:
(x + -0.4285714286)(x + -0.4285714286) = 3.4693877554

Calculate the square root of the right side: 1.862629259

Break this problem into two subproblems by setting 
(x + -0.4285714286) equal to 1.862629259 and -1.862629259.

Subproblem 1

x + -0.4285714286 = 1.862629259 Simplifying x + -0.4285714286 = 1.862629259 Reorder the terms: -0.4285714286 + x = 1.862629259 Solving -0.4285714286 + x = 1.862629259 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4285714286' to each side of the equation. -0.4285714286 + 0.4285714286 + x = 1.862629259 + 0.4285714286 Combine like terms: -0.4285714286 + 0.4285714286 = 0.0000000000 0.0000000000 + x = 1.862629259 + 0.4285714286 x = 1.862629259 + 0.4285714286 Combine like terms: 1.862629259 + 0.4285714286 = 2.2912006876 x = 2.2912006876 Simplifying x = 2.2912006876

Subproblem 2

x + -0.4285714286 = -1.862629259 Simplifying x + -0.4285714286 = -1.862629259 Reorder the terms: -0.4285714286 + x = -1.862629259 Solving -0.4285714286 + x = -1.862629259 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4285714286' to each side of the equation. -0.4285714286 + 0.4285714286 + x = -1.862629259 + 0.4285714286 Combine like terms: -0.4285714286 + 0.4285714286 = 0.0000000000 0.0000000000 + x = -1.862629259 + 0.4285714286 x = -1.862629259 + 0.4285714286 Combine like terms: -1.862629259 + 0.4285714286 = -1.4340578304 x = -1.4340578304 Simplifying x = -1.4340578304

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.2912006876, -1.4340578304}

See similar equations:

| 7x^2-37x+10=0 | | x^2-16x-192=0 | | 2x^3+4x^2+96x=0 | | -22=-7w+5(w-2) | | 11n-2=6n-47 | | 4x-15=9x | | 5x^2-23+12=0 | | 4v+4=-12 | | 22y^2-47y+25=0 | | x+2(x-2)=4(x-4)+14 | | -4(u+7)=-6u-22 | | 2x-6-3+2(2x+8)=4x-1 | | 3x^2+8x+12=0 | | 12y^2+5y-3=0 | | 2=2x+8 | | -6x+4(x+2)=-8 | | 86-6(x-5)=29(x-1) | | 45-(2x+4)=2(x+3)+x | | 9(x-2)+5x-10x+3+6x+15=0 | | 5x+2(x+2)=2(x+12) | | 11x-5500=0 | | 0=2x^4-2x^2-40 | | 8x+46=3x+6 | | x+x+5=9 | | 3+4(3x+6)+3=5+2(2x+5)-3x | | -8x+2=-38 | | 2c^2=13c+7 | | 4z-10=-46 | | 2x^3-11x^2=-5x | | -7+5y=-17 | | -4x+30=18 | | 340-45x=40+5x |

Equations solver categories