Solve the following quadratic equation using square roots: −9+(x−3)2−4=−4
−9+(x−3)2−4=−4 can be rewritten as (x-3)^2 -4 = 0.
To solve this quadratic equation, we can isolate (x-3)^2 by adding 4 to both sides: (x-3)^2 = 4.
Next, we take the square root of both sides to eliminate the square: x-3 = ±2.
Now, we can solve for x by adding 3 to both sides: x = 3±2.
Therefore, the solutions to the quadratic equation are x = 5 and x = 1.
To solve the quadratic equation −9+(x−3)²−4=−4 using square roots, we can follow these steps:
Step 1: Simplify the equation by expanding the square on the left side.
-9 + (x - 3)² - 4 = -4
-9 + (x - 3)(x - 3) - 4 = -4
-9 + (x² - 6x + 9) - 4 = -4
Step 2: Combine like terms on the left side.
-13 + x² - 6x + 9 = -4
Step 3: Simplify further.
x² - 6x - 4 = -4 + 13
x² - 6x - 4 = 9
Step 4: Move all terms to one side to get a quadratic equation in standard form.
x² - 6x - 4 - 9 = 0
x² - 6x - 13 = 0
Now that we have the quadratic equation x² - 6x - 13 = 0, we can proceed to find the solutions using the quadratic formula or completing the square.
To solve the quadratic equation using square roots, we need to isolate the squared term first.
Given the equation: -9 + (x-3)^2 - 4 = -4
1. Combine the constants on the left side of the equation:
-9 - 4 = -4 + (x-3)^2
-13 = -4 + (x-3)^2
2. Move the constant term to the right side of the equation:
(x-3)^2 = -13 + 4
(x-3)^2 = -9
3. Take the square root of both sides of the equation:
√(x-3)^2 = ±√(-9)
x-3 = ±√(-9)
4. Since the square root of a negative number is not a real number, the equation does not have real solutions.
Therefore, the quadratic equation -9 + (x-3)^2 - 4 = -4 has no real solutions.