Solve the quadratic equation by the square root property.
(2x + 5)2 = 49
A. {-6, 1}
B. {0, 1}
C. {-27, 27}
D. {1, 6}
d?
type powers this way:
(2x+5)^2 = 49
so
2x+5 = ±7
2x = 2 or 2x = -12
x = 1 or x = -6
Thank you
To solve the quadratic equation using the square root property, we need to isolate the squared term and then take the square root of both sides of the equation.
Here's how you can solve the equation (2x + 5)^2 = 49 using the square root property:
Step 1: Expand the squared term:
(2x + 5)^2 = 49
4x^2 + 20x + 25 = 49
Step 2: Subtract 49 from both sides to isolate the quadratic term:
4x^2 + 20x + 25 - 49 = 0
4x^2 + 20x - 24 = 0
Step 3: Now, apply the square root property:
Take the square root of both sides of the equation to eliminate the square term:
√(4x^2 + 20x - 24) = ±√0
Step 4: Simplify the equation:
√(4x^2 + 20x - 24) = 0
Step 5: Solve for x:
Now, set up two equations by removing the square root on the left side:
2x + 5 = 0 or 2x + 5 = 0
Solving the first equation:
2x + 5 = 0
2x = -5
x = -5/2
Solving the second equation:
2x + 5 = 0
2x = -5
x = -5/2
Therefore, the solutions to the quadratic equation (2x + 5)^2 = 49 are x = -5/2.
The options you provided are A. {-6, 1}, B. {0, 1}, C. {-27, 27}, and D. {1, 6}. None of these options match the solution for the given equation. Therefore, the correct answer is none of the provided options.