Solve the equation by completing the square. x² – 7x – 4 = 0
• 7.53, –0.53
• –7.53, –0.53
• –7.53, 0.53
• 7.53, 0.53
The answer is A *
x^2 - 7x - 4
x^2 - 7x + (7/2)^2 - 4 - (7/2)^2
(x - 7/2)^2 - 65/4
y=0 when
x - 7/2 = ±√65/2
x = (7±√65)/2
x = 7.53 or -.53
Why did the math book go to the therapist? Because it had too many problems.
To solve the equation x² – 7x – 4 = 0 by completing the square, we need to follow these steps:
Step 1: Move the constant term to the other side of the equation:
x² – 7x = 4
Step 2: Take half of the coefficient of x (-7) and square it:
(-7/2)² = 49/4
Step 3: Add the result of Step 2 to both sides of the equation:
x² – 7x + 49/4 = 4 + 49/4
x² – 7x + 49/4 = 65/4
Step 4: Rewrite the left side of the equation as a perfect square trinomial and simplify the right side:
(x – 7/2)² = 65/4
Step 5: Take the square root of both sides and solve for x:
x – 7/2 = ±√(65/4)
x = 7/2 ± √(65/4)
So the solutions to the equation are:
x = 7/2 + √(65/4) ≈ 7.53
x = 7/2 - √(65/4) ≈ -0.53
Therefore, the correct answer is: 7.53, -0.53
To solve the equation x² – 7x – 4 = 0 by completing the square, follow these steps:
Step 1: Move the constant term to the other side of the equation:
x² - 7x = 4
Step 2: Take half of the coefficient of x (in this case, -7), square it, and add it to both sides of the equation:
x² - 7x + (-7/2)² = 4 + (-7/2)²
x² - 7x + 49/4 = 4 + 49/4
Step 3: Simplify the right side of the equation:
x² - 7x + 49/4 = (16+49)/4
x² - 7x + 49/4 = 65/4
Step 4: Rewrite the left side of the equation as a perfect square trinomial:
(x - 7/2)² = 65/4
Step 5: Take the square root of both sides of the equation:
x - 7/2 = ± √(65/4)
Step 6: Solve for x:
x = 7/2 ± √(65/4)
Step 7: Simplify the expression:
x = 7/2 ± √(65)/2
So, the solutions to the equation x² - 7x - 4 = 0, solved by completing the square, are:
x = 7/2 + √(65)/2 and x = 7/2 - √(65)/2
Approximately, the solutions are:
x ≈ 7.53 and x ≈ -0.53
To solve the equation x² – 7x – 4 = 0 by completing the square, you can follow these steps:
1. Move the constant term to the right side of the equation:
x² – 7x = 4
2. Take half of the coefficient of the x-term and square it. Add this value to both sides of the equation:
x² – 7x + (7/2)² = 4 + (7/2)²
Simplifying:
x² – 7x + 49/4 = 4 + 49/4
3. Factor the left side of the equation (a perfect square trinomial):
(x – 7/2)² = 63/4 + 49/4
Simplifying:
(x – 7/2)² = 112/4
4. Simplify the right side of the equation:
(x – 7/2)² = 28
5. Take the square root of both sides of the equation:
x – 7/2 = ±√28
6. Simplify the square root of 28:
x – 7/2 = ±√4 * √7
x – 7/2 = ±2√7
7. Solve for x:
x = 7/2 ± 2√7
So the solutions to the equation x² – 7x – 4 = 0, after completing the square, are x = 7/2 + 2√7 and x = 7/2 - 2√7.