completing the square root Please solve this, x² + 5x - 45 = 0
Answer (1)
Answer:Certainly! Here's how to complete the square on the given quadratic equation:1. Move the constant term to the right side of the equation:x² + 5x = 452. Take half of the coefficient of x (in this case, 5) and square it. Then, add and subtract the resulting quantity to both sides of the equation:x² + 5x + (5/2)² - (5/2)² = 45 - (5/2)²3. Simplify the expression on the left side and solve for x:(x + 5/2)Step-by-step explanation:Here's the complete solution:x = (-b ± √(b² - 4ac)) / 2ax = (-5 ± √(5² - 4(-45)(1))) / 2(1)x = (-5 ± √(25 + 180)) / 2x = (-5 ± √205) / 2x = (-5 ± 14.23) / 2x = (-9.23, 4.77)So, the solutions are x = -9.23 and x = 4.77.It's important to note that this method of solving quadratic equations by completing the square only works when the coefficient of x² is 1. If the coefficient of x² is not 1, you will need to factor the polynomial first before proceeding with this method.The answer is -9.23 and 4.77.
