Procedure for Completing the Square Get equation in the form x2 + bx = c (x2 and x terms on left, number on right) Find the needed number to complete the square nn = Add it to both sides. Factor the perfect square. Write it as a square that looks like (x + b/2)2 Square root both sides Solve for x Ex f Solve: x2 8x 2 = 0 – – Exg Solve: 4x2 40x - 300 = 0 (similar to Ex f, with Khan video) – Ex h Solve 3k2 + k + 2 = 0 (This is nasty) 11.2 Quadratic Formula Recall: Quadratic equations have the standard form ax2 + bx + c = 0 Quadratic equations have 2, 1, or 0 real solutions Ex a Find a, b, and c for the equations: 3x2 2 = 5x – x2 17 = 0 –
Procedure for Completing the Square Get equation in the form x2 + bx = c (x2 and x terms on left, number on right) Find the needed number to complete the square nn = Add it to both sides. Factor the perfect square. Write it as a square that looks like (x + b/2)2 Square root both sides Solve for x Ex f Solve: x2 – 8x – 2 = 0 Exg Solve: 4x2 – 40x - 300 = 0 (similar to Ex f, with Khan video) Ex h Solve 3k2 + k + 2 = 0 (This is nasty) 11.2 Quadratic Formula Recall: Quadratic equations have the standard form ax2 + bx + c = 0 Quadratic equations have 2, 1, or 0 real solutions Ex a Find a, b, and c for the equations: 3x2 – 2 = 5x x2 – 17 = 0