Final answer:
To solve the given equations using the square roots method, you need to isolate the variable x and take the square root of both sides. Let's go through the step-by-step solutions for each equation.
Step-by-step explanation:
To solve the given equations using the square roots method, we need to isolate the variable x and take the square root of both sides. Here are the step-by-step solutions for each equation:
14. (x+4)^2 = -9016
Expand the equation:
(x+4)(x+4) = -9016
x^2 + 8x + 16 = -9016
Subtract 16 from both sides:
x^2 + 8x + 16 - 16 = -9016 - 16
x^2 + 8x = -9032
Take the square root of both sides:
√(x^2 + 8x) = ±√(-9032)
x = ±√(-9032)
The square root of -9032 is not a real number, so there is no solution for this equation.
18. 5(x-3)^2 = -225
Divide both sides by 5:
(x-3)^2 = -45
Take the square root of both sides:
x-3 = ±√(-45)
x-3 = ±i√(45)
√(45) = 3√5, so the solutions are:
x = 3 ± 3i√5
20. -5/2(x+1)^2 = 30
Multiply both sides by -2/5:
(x+1)^2 = -12
Take the square root of both sides:
x+1 = ±√(-12)
x+1 = ±i√(12)
x+1 = ±i√(4*3)
x+1 = ±2i√3
Solve for x:
x = -1 ± 2i√3