Final answer:
To find the solutions to the equation x²+6x+9=20, use the quadratic formula and simplify the equation, giving two solutions: x = -3 + 2√5 and x = -3 - 2√5.
Step-by-step explanation:
To find the solutions to the equation x²+6x+9=20, we need to solve for x. First, let's simplify the equation: x²+6x+9-20=0. Combine like terms: x²+6x-11=0. Now, we can use the quadratic formula to solve for x: x = (-b ± √(b²-4ac)) / (2a). Plugging in the values a=1, b=6, c=-11 into the formula, we get two solutions for x: x = (-6 ± √(6²-4(1)(-11))) / (2(1)). Simplifying further, x = (-6 ± √(36+44)) / 2, x = (-6 ± √(80)) / 2, x = (-6 ± √(16*5)) / 2, x = (-6 ± 4√5) / 2, x = -3 ± 2√5. Therefore, the solutions to the equation are x = -3 + 2√5 and x = -3 - 2√5.