Solve the following quadratic equation using square roots: (x+3)^2=36 .
To solve the quadratic equation (x+3)^2 = 36 using square roots, we need to isolate x.
Taking the square root of both sides of the equation, we have:
√((x+3)^2) = √36
Simplifying the square root on the left side, we get:
|x+3| = √36
The square root of 36 is 6, so we have:
|x+3| = 6
Now we can solve for x by considering both the positive and negative cases:
1. Positive case:
If |x+3| = 6, then x+3 = 6
Solving for x, we subtract 3 from both sides:
x = 6 - 3
x = 3
2. Negative case:
If |x+3| = 6, then x+3 = -6
Solving for x, we subtract 3 from both sides:
x = -6 - 3
x = -9
So the solutions to the quadratic equation (x+3)^2 = 36 are x = 3 and x = -9.
To solve the quadratic equation (x+3)^2 = 36 using square roots, we can first take the square root of both sides to eliminate the square.
√((x+3)^2) = √36
Taking the square root of (x+3)^2 gives us two possible solutions since taking the square root of a number can be positive or negative:
x + 3 = ±√36
Now, let's simplify the square root of 36:
x + 3 = ±6
To solve for x, we need to isolate the variable. Let's solve for x in both cases:
Case 1: x + 3 = 6
Subtract 3 from both sides:
x = 6 - 3
x = 3
Case 2: x + 3 = -6
Subtract 3 from both sides:
x = -6 - 3
x = -9
Therefore, the solutions to the quadratic equation (x+3)^2 = 36 are x = 3 and x = -9.
To solve the quadratic equation (x+3)^2 = 36 using square roots, we need to isolate x on one side of the equation and then take the square root of both sides. Here's the step-by-step process:
1. Expand the left side of the equation by squaring the binomial (x+3)^2:
(x+3)(x+3) = 36
x^2 + 3x + 3x + 9 = 36
x^2 + 6x + 9 = 36
2. Move the constant term to the right side of the equation:
x^2 + 6x = 36 - 9
x^2 + 6x = 27
3. Now, we can isolate x on the left side by subtracting 27 from both sides:
x^2 + 6x - 27 = 0
4. Now, we can use the quadratic formula to find the values of x:
The quadratic formula is given by: x = (-b ± √(b^2 - 4ac)) / (2a)
For our equation, a = 1, b = 6, and c = -27.
Substituting these values into the formula, we have:
x = ( -6 ± √((6^2) - 4(1)(-27)) ) / (2(1))
5. Simplify the equation.
x = ( -6 ± √(36 + 108)) / 2
x = ( -6 ± √(144)) / 2
x = ( -6 ± 12) / 2
6. Solve for two possible values of x:
a. x = ( -6 + 12 ) / 2
x = 6 / 2
x = 3
b. x = ( -6 - 12 ) / 2
x = -18 / 2
x = -9
So, the solution to the quadratic equation (x+3)^2 = 36 using square roots is x = 3 and x = -9.