Solve for x in the equation 3x²+18x+15=0 using complete square method
To solve the equation 3x²+18x+15=0 using the complete the square method, let's follow these steps:
1. Divide the entire equation by 3 to simplify the equation: x² + 6x + 5 = 0
2. Move the constant term (5) to the right side of the equation: x² + 6x = -5
3. Take half of the coefficient of x (6/2 = 3) and square it to complete the square: (x + 3)² = -5 + 9
4. Simplify the right side of the equation: (x + 3)² = 4
5. Take the square root of both sides of the equation: √[(x + 3)²] = ±√4
6. Remove the square root by taking both positive and negative roots: x + 3 = ±2
7. Solve for x by subtracting 3 from both sides: x = -3 ± 2
The solution to the equation 3x² + 18x + 15 = 0 using the complete square method is x = -1 or x = -5.
To solve the quadratic equation 3x² + 18x + 15 = 0 using the complete the square method, follow these steps:
Step 1: Divide the entire equation by the coefficient of x², which is 3 in this case, to make the coefficient 1:
x² + (18/3)x + 15/3 = 0
Simplifying the equation gives:
x² + 6x + 5 = 0
Step 2: Move the constant term, 5, to the right side of the equation:
x² + 6x = -5
Step 3: Take half of the coefficient of x (6) and square it:
(1/2 * 6)² = (3)² = 9
Step 4: Add the result from step 3 to both sides of the equation:
x² + 6x + 9 = -5 + 9
Simplifying the equation gives:
x² + 6x + 9 = 4
Step 5: Rewrite the left side of the equation as a perfect square:
(x + 3)² = 4
Step 6: Take the square root of both sides of the equation, remembering to include both positive and negative square roots:
x + 3 = ±√4
x + 3 = ±2
Step 7: Solve for x:
x = -3 + 2
x = -1
x = -3 - 2
x = -5
The solutions to the equation 3x² + 18x + 15 = 0 are x = -1 and x = -5.