(z^2)+5z-7=0

Simple and best practice solution for (z^2)+5z-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 (z^2)+5z-7=0 equation:


Simplifying
(z2) + 5z + -7 = 0
z2 + 5z + -7 = 0

Reorder the terms:
-7 + 5z + z2 = 0

Solving
-7 + 5z + z2 = 0

Solving for variable 'z'.

Begin completing the square.

Move the constant term to the right:

Add '7' to each side of the equation.
-7 + 5z + 7 + z2 = 0 + 7

Reorder the terms:
-7 + 7 + 5z + z2 = 0 + 7

Combine like terms: -7 + 7 = 0
0 + 5z + z2 = 0 + 7
5z + z2 = 0 + 7

Combine like terms: 0 + 7 = 7
5z + z2 = 7

The z term is 5z.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5z + 6.25 + z2 = 7 + 6.25

Reorder the terms:
6.25 + 5z + z2 = 7 + 6.25

Combine like terms: 7 + 6.25 = 13.25
6.25 + 5z + z2 = 13.25

Factor a perfect square on the left side:
(z + 2.5)(z + 2.5) = 13.25

Calculate the square root of the right side: 3.640054945

Break this problem into two subproblems by setting 
(z + 2.5) equal to 3.640054945 and -3.640054945.

Subproblem 1

z + 2.5 = 3.640054945 Simplifying z + 2.5 = 3.640054945 Reorder the terms: 2.5 + z = 3.640054945 Solving 2.5 + z = 3.640054945 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + z = 3.640054945 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + z = 3.640054945 + -2.5 z = 3.640054945 + -2.5 Combine like terms: 3.640054945 + -2.5 = 1.140054945 z = 1.140054945 Simplifying z = 1.140054945

Subproblem 2

z + 2.5 = -3.640054945 Simplifying z + 2.5 = -3.640054945 Reorder the terms: 2.5 + z = -3.640054945 Solving 2.5 + z = -3.640054945 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + z = -3.640054945 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + z = -3.640054945 + -2.5 z = -3.640054945 + -2.5 Combine like terms: -3.640054945 + -2.5 = -6.140054945 z = -6.140054945 Simplifying z = -6.140054945

Solution

The solution to the problem is based on the solutions from the subproblems. z = {1.140054945, -6.140054945}

See similar equations:

| B=a/20 | | (3c^2d^(1/2))^-2(2d^2c^(-1/2))^-1 | | t^2=0.0001 | | b^2=0b-15 | | 14/4n^-6 | | 0.0001=t^2 | | Log^4(x+5)=2 | | w^2-18w=-72 | | 3x+3=9x+21 | | (z^2)+11z-468=0 | | -4-(1/9) | | -66=-6(8x+3) | | (z^2)+z-28=0 | | (1/9)-9y=-4 | | 7x-5+x=7 | | (x^6y^2)/(x^6y^3) | | v/7+13=20 | | 0.8x-0.3x-3=4 | | 5x-x^2-1=0 | | h^2-6h=31 | | (z^2)+12z+19=0 | | Y=-0.1x^2+10x | | 2(7x+3)=6 | | 92000+2.10x=15x | | 18+q=-32 | | 5x/x-7-3x/x-2 | | z^2+16z-29=0 | | -19+h=25 | | -8+3=-5 | | (z^2)-12z+19=0 | | -19h+h=25 | | (-3/5)=(2/3u)-(1/4) |

Equations solver categories