4w^2+6w-7=0

Simple and best practice solution for 4w^2+6w-7=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 4w^2+6w-7=0 equation:


Simplifying
4w2 + 6w + -7 = 0

Reorder the terms:
-7 + 6w + 4w2 = 0

Solving
-7 + 6w + 4w2 = 0

Solving for variable 'w'.

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

Divide each side by '4'.
-1.75 + 1.5w + w2 = 0

Move the constant term to the right:

Add '1.75' to each side of the equation.
-1.75 + 1.5w + 1.75 + w2 = 0 + 1.75

Reorder the terms:
-1.75 + 1.75 + 1.5w + w2 = 0 + 1.75

Combine like terms: -1.75 + 1.75 = 0.00
0.00 + 1.5w + w2 = 0 + 1.75
1.5w + w2 = 0 + 1.75

Combine like terms: 0 + 1.75 = 1.75
1.5w + w2 = 1.75

The w term is 1.5w.  Take half its coefficient (0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
1.5w + 0.5625 + w2 = 1.75 + 0.5625

Reorder the terms:
0.5625 + 1.5w + w2 = 1.75 + 0.5625

Combine like terms: 1.75 + 0.5625 = 2.3125
0.5625 + 1.5w + w2 = 2.3125

Factor a perfect square on the left side:
(w + 0.75)(w + 0.75) = 2.3125

Calculate the square root of the right side: 1.520690633

Break this problem into two subproblems by setting 
(w + 0.75) equal to 1.520690633 and -1.520690633.

Subproblem 1

w + 0.75 = 1.520690633 Simplifying w + 0.75 = 1.520690633 Reorder the terms: 0.75 + w = 1.520690633 Solving 0.75 + w = 1.520690633 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + w = 1.520690633 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + w = 1.520690633 + -0.75 w = 1.520690633 + -0.75 Combine like terms: 1.520690633 + -0.75 = 0.770690633 w = 0.770690633 Simplifying w = 0.770690633

Subproblem 2

w + 0.75 = -1.520690633 Simplifying w + 0.75 = -1.520690633 Reorder the terms: 0.75 + w = -1.520690633 Solving 0.75 + w = -1.520690633 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + w = -1.520690633 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + w = -1.520690633 + -0.75 w = -1.520690633 + -0.75 Combine like terms: -1.520690633 + -0.75 = -2.270690633 w = -2.270690633 Simplifying w = -2.270690633

Solution

The solution to the problem is based on the solutions from the subproblems. w = {0.770690633, -2.270690633}

See similar equations:

| 2x+6=21-3 | | 2x-x+5x-9= | | 0.6a+5-0.3a-7= | | 2y-3.5=6.5 | | 5z=2.9+3.6 | | m^2+3m-3=0 | | 0=y^2+2y-96 | | 5=5-5t | | 3x-21=5x-5 | | -4x+-4-9=-12x+11 | | 35=8-9y | | -p^2-2p=0 | | 2(j-7)=64 | | 3y-8=9 | | 2x+4(x+3)=36 | | 4e^3x+6=30 | | -3x-3x=26-2 | | 8c-13=3c+36 | | 2u^2-3u=0 | | -9=k-5k+7 | | 4x^2-15=25 | | 6t+17-3t=38 | | -6w+14=-76 | | 11x+22x-2y+54y= | | 0.5a-5-0.5a= | | -f^2+5f=0 | | 3-8p=29 | | 6(x+3)-9(x-1)=5-(X+3) | | 6t+17-3r=38 | | n-2n=n-4 | | 7r^2-5=0 | | G+14.8=45 |

Equations solver categories