Solve the following quadratic equation using square roots: (x+3)^2=36 .
Only give one answer
Taking the square root of both sides of the equation, we have:
√((x+3)^2) = √36
Simplifying the left side of the equation, we have:
x + 3 = ±√36
Since we only need one answer, we can take the positive square root:
x + 3 = √36
Simplifying further, we have:
x + 3 = 6
Subtracting 3 from both sides of the equation, we have:
x = 6 - 3
x = 3
Therefore, the solution to the quadratic equation (x+3)^2 = 36 is x = 3.
To solve the quadratic equation (x+3)^2 = 36 using square roots, follow these steps:
Step 1: Take the square root of both sides of the equation.
√[(x+3)^2] = √36
Step 2: Simplify the square root on the left side.
x + 3 = ±√36
Step 3: Simplify the square root on the right side.
x + 3 = ±6
Step 4: Solve for x by subtracting 3 from both sides.
x = -3 ± 6
Simplifying the expression, we have two possible solutions:
x = -3 + 6 = 3
x = -3 - 6 = -9
Therefore, the quadratic equation (x+3)^2 = 36 has two solutions: x = 3 and x = -9.
To solve the given quadratic equation using square roots, we need to isolate the variable x.
Step 1: Expand the equation
(x+3)^2 = 36
x^2 + 6x + 9 = 36
Step 2: Move the constant term to the right side of the equation
x^2 + 6x = 36 - 9
x^2 + 6x = 27
Step 3: Set the equation equal to zero
x^2 + 6x - 27 = 0
Step 4: Use the quadratic formula to find the values of x
The quadratic formula is x = (-b ± √(b^2 - 4ac)) / (2a).
For our equation, a = 1, b = 6, and c = -27.
x = (-6 ± √(6^2 - 4(1)(-27))) / (2 * 1)
x = (-6 ± √(36 + 108)) / 2
x = (-6 ± √144) / 2
x = (-6 ± 12) / 2
Step 5: Simplify the equation
For x = (-6 + 12) / 2, we get x = 6 / 2 = 3.
For x = (-6 - 12) / 2, we get x = -18 / 2 = -9.
Therefore, the solution to the quadratic equation (x+3)^2 = 36 is x = 3.