Completing square

Number 9.) 8x² + 16x = 42 {3 over 2, negative 7 over 2}

Number 10.) n² – 2n – 3 = 0 {3, negative 1}

Answer:8x² + 16x = 42To complete the square, we need to find a constant that makes the left side a perfect square trinomial. The constant will be half the coefficient of x squared divided by the coefficient of x.In this case, the coefficient of x is 16, so we need to find a constant that makes (8x + k)² a perfect square.(8x + k)² = 8x² + 16xk + k²To make this a perfect square, we need k² + 16k = 16, so k = -8.Now, we can rewrite the equation as:8x² + 16x + 64 = 42 + 648(x² + 2x) = 1068(x + 1)² = 106x + 1 = ±√(106/8)x = -1 ± √(106/8)Therefore, the solutions are:x = (-1 + √(106/8)) / 2 = 3/2x = (-1 - √(106/8)) / 2 = -7/2n² – 2n – 3 = 0To complete the square, we need to find a constant that makes the left side a perfect square trinomial. The constant will be half the coefficient of n squared divided by the coefficient of n.In this case, the coefficient of n is -2, so we need to find a constant that makes (n - k)² a perfect square.(n - k)² = n² - 2nk + k²To make this a perfect square, we need k² - 2k = -2, so k = 1.Now, we can rewrite the equation as:n² - 2n + 1 - 3 = 0(n - 1)² - 2 = 0(n - 1)² = 2n - 1 = ±√2Therefore, the solutions are:n = 1 + √2n = 1 - √2Simplifying, we get:n = 3n = -1

Answered by givenalindayo21 | 2024-09-02