Final answer:
To solve the equation (x+7)²=2x²+5x+69, we can expand, combine like terms, and use the quadratic formula to find the solutions for x.
Step-by-step explanation:
In order to solve the equation (x+7)²=2x²+5x+69, we need to expand the squared term on the left side of the equation. This gives us x²+14x+49=2x²+5x+69.
Next, we need to combine like terms and move everything to one side of the equation. This gives us x²+9x-20=0.
Finally, we can use the quadratic formula to solve for x. The quadratic formula is x=(-b±√(b²-4ac))/(2a), where a, b, and c are the coefficients of the quadratic equation. Plugging in the values from our equation, we get x=(-9±√(81+80))/(2*1). Simplifying further, we have x=(-9±√(161))/(2).