32x^2+16x-51=0

Simple and best practice solution for 32x^2+16x-51=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 32x^2+16x-51=0 equation:


Simplifying
32x2 + 16x + -51 = 0

Reorder the terms:
-51 + 16x + 32x2 = 0

Solving
-51 + 16x + 32x2 = 0

Solving for variable 'x'.

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

Divide each side by '32'.
-1.59375 + 0.5x + x2 = 0

Move the constant term to the right:

Add '1.59375' to each side of the equation.
-1.59375 + 0.5x + 1.59375 + x2 = 0 + 1.59375

Reorder the terms:
-1.59375 + 1.59375 + 0.5x + x2 = 0 + 1.59375

Combine like terms: -1.59375 + 1.59375 = 0.00000
0.00000 + 0.5x + x2 = 0 + 1.59375
0.5x + x2 = 0 + 1.59375

Combine like terms: 0 + 1.59375 = 1.59375
0.5x + x2 = 1.59375

The x term is 0.5x.  Take half its coefficient (0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
0.5x + 0.0625 + x2 = 1.59375 + 0.0625

Reorder the terms:
0.0625 + 0.5x + x2 = 1.59375 + 0.0625

Combine like terms: 1.59375 + 0.0625 = 1.65625
0.0625 + 0.5x + x2 = 1.65625

Factor a perfect square on the left side:
(x + 0.25)(x + 0.25) = 1.65625

Calculate the square root of the right side: 1.286953768

Break this problem into two subproblems by setting 
(x + 0.25) equal to 1.286953768 and -1.286953768.

Subproblem 1

x + 0.25 = 1.286953768 Simplifying x + 0.25 = 1.286953768 Reorder the terms: 0.25 + x = 1.286953768 Solving 0.25 + x = 1.286953768 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = 1.286953768 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = 1.286953768 + -0.25 x = 1.286953768 + -0.25 Combine like terms: 1.286953768 + -0.25 = 1.036953768 x = 1.036953768 Simplifying x = 1.036953768

Subproblem 2

x + 0.25 = -1.286953768 Simplifying x + 0.25 = -1.286953768 Reorder the terms: 0.25 + x = -1.286953768 Solving 0.25 + x = -1.286953768 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = -1.286953768 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = -1.286953768 + -0.25 x = -1.286953768 + -0.25 Combine like terms: -1.286953768 + -0.25 = -1.536953768 x = -1.536953768 Simplifying x = -1.536953768

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.036953768, -1.536953768}

See similar equations:

| -4+x=17.1 | | 96x^2-48x-153=0 | | 4(3x-5y)+3(x-y)= | | (x+1)(x-s)=0 | | 15=-log(0.5)-log(x) | | 15n^3+25n= | | x+(-6)=62.8 | | 15x/5x-3 | | 15x/5s-3 | | y=2*(x^2+x-12) | | 5x-15=3x+1 | | 4x^4+24x^3= | | 49x1/10 | | 0.2m+2.1m=46 | | 8z^2+cz+35=(4z+7)(2z+5)whatisc | | x+11.6=4 | | 112x+16=115x | | 5d^6+2d^5= | | 7w^5-35w^2= | | 6p-(p+3)=7 | | f(x)=x^2-5x+6 | | x^2-15=49 | | 8-12sin^2x=4cos^2x | | 9m^7-3m^2= | | 5x-(3a+4)+3(a-1)= | | 25+x^2=50 | | 6(x+1)=6x+10 | | -8x+7y=0 | | (r-8)(r+5)= | | 5(5)=4x(x) | | 7x^2-9x-8+2x= | | -3.6-1.4p=-5p-(-5p+3) |

Equations solver categories