find the solutions of x²+3x-18=0 by completing the square.
Answer (1)
Answer:x² + 3x - 18 = 0•move the constant term to the right side of the equation. x² + 3x = 18•take half of the coefficient of the x term (which is 3), square it (3/2)² = 9/4, and add it to the both sides of the equation. x² + 3x + 9/4 = 18 + 9/4•the left side of the equation is now a perfect square trinomial. (x + 3/2)² = 81/4•take the square root of both sides. √(x + 3/2)² = √81/4•simplify and solve for x: x + 3/2 = ±9/2 x + 3/2 = 9/2 x = 9/2 - 3/2 x = 6/2 ÷ 2/2 x1 = 3 x + 3/2 = -9/2 x = -9/2 - 3/2 x = -12/2 ÷ 2/2 x2 = -6Therefore, the solutions for x² + 3x - 18 = 0 are x1 = 3 and x2 = -6. checking:x1 = 3x² + 3x - 18 = 0(3)² + 3(3) - 18 = 09 + 9 - 18 = 018 - 18 = 00 = 0✔️x2 = -6x² + 3x - 18 = 0(-6)² + 3(-6) - 18 = 036 - 18 - 18 = 018 - 18 = 00 = 0 ✔️
