i forgot how to solve problems like this...

2x^2-18x=0, x^2=6x+7, 6y^2+5y-6=0

also I need help on this one

SOLVE FOR X CORRECT TO 4 DECIMAL PLACES

x^2+6x+2=0 2x+4=3x^2

2x^2-18x=0

try to factor first
2x (x-9) = 0
so x = 0 or x = 9

x^2=6x+7
x^2 -6 x - 7 = 0
(x-7)(x+1) = 0
so x = 7 or x = -1

6y^2+5y-6=0
(6x-1)(x+1) = 0
x = 1/6 or x = -1

x^2+6x+2=0
if you can not factor, complete the square or use the quadratic equation
x = [ -b +/- sqrt (b^2 - 4 a c) ] / 2a
x = [ -6 +/- sqrt (36 - 8) ] / 2
use calculator to 4 places

To solve the equations provided, I will demonstrate the step-by-step process for each one.

1. Solving the equation 2x^2 - 18x = 0:
Step 1: Factor out the common term, x: x(2x - 18) = 0.
Step 2: Set each factor equal to zero and solve for x:
a) x = 0.
b) 2x - 18 = 0.
Simplifying, we get 2x = 18, and dividing by 2 gives x = 9.
Therefore, the solution to the equation is x = 0 and x = 9.

2. Solving the equation x^2 = 6x + 7:
Step 1: Rearrange the equation to bring all terms to one side:
x^2 - 6x - 7 = 0.
Step 2: Factor the quadratic equation or use the quadratic formula to solve for x.
In this case, let's use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a),
where a = 1, b = -6, and c = -7.
Plugging in the values:
x = (-(-6) ± √((-6)^2 - 4 * 1 * (-7))) / (2 * 1).
Simplifying further:
x = (6 ± √(36 + 28)) / 2.
x = (6 ± √64) / 2.
x = (6 ± 8) / 2.
This yields two solutions:
a) x = (6 + 8) / 2 = 14 / 2 = 7.
b) x = (6 - 8) / 2 = -2 / 2 = -1.
Therefore, the solutions to the equation are x = 7 and x = -1.

3. Solving the equation 6y^2 + 5y - 6 = 0:
Step 1: Factor the quadratic equation or use the quadratic formula to solve for y.
Let's factor this equation:
(3y + 6)(2y - 1) = 0.
Step 2: Set each factor equal to zero and solve for y:
a) 3y + 6 = 0.
Simplifying, we get 3y = -6, and dividing by 3 gives y = -2.
b) 2y - 1 = 0.
Simplifying, we get 2y = 1, and dividing by 2 gives y = 1/2.
Therefore, the solutions to the equation are y = -2 and y = 1/2.

4. Solving the equation x^2 + 6x + 2 = 0:
Step 1: Use the quadratic formula to solve for x:
x = (-b ± √(b^2 - 4ac)) / (2a),
where a = 1, b = 6, and c = 2.
Plugging in the values:
x = (-(6) ± √((6)^2 - 4 * 1 * (2))) / (2 * 1).
Simplifying further:
x = (-6 ± √(36 - 8)) / 2.
x = (-6 ± √28) / 2.
x = (-6 ± 2√7) / 2.
Simplifying the expression:
x = -3 ± √7.
Therefore, the solutions to the equation when rounded to 4 decimal places are x ≈ -3 + √7 and x ≈ -3 - √7.

5. Solving the equation 2x + 4 = 3x^2:
Step 1: Rearrange the equation to bring all terms to one side:
3x^2 - 2x - 4 = 0.
Step 2: Factor the quadratic equation or use the quadratic formula to solve for x.
In this case, let's use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a),
where a = 3, b = -2, and c = -4.
Plugging in the values:
x = (-(2) ± √((-2)^2 - 4 * 3 * (-4))) / (2 * 3).
Simplifying further:
x = (-2 ± √(4 + 48)) / 6.
x = (-2 ± √52) / 6.
Simplifying the expression:
x = (-1 ± √13) / 3.
Therefore, the solutions to the equation when rounded to 4 decimal places are x ≈ (-1 + √13) / 3 and x ≈ (-1 - √13) / 3.

I hope this explanation helps you understand how to solve these types of problems!