Question

Show how to work out the exact solutions of 4(x+7)^2=25

Answer 1

Answers: -9/2 and -19/2

Work Shown

`4(\text{x}+7)^2 = 25\\\\(\text{x}+7)^2 = (25)/(4)\\\\\sqrt{(\text{x}+7)^2} = \sqrt{(25)/(4)}\\\\|\text{x}+7| = (√(25))/(√(4))\\\\|\text{x}+7| = (5)/(2)\\\\\text{x}+7 = \pm(5)/(2)\\\\`

`\text{x}+7 = (5)/(2) \ \text{ or } \ \text{x}+7 = -(5)/(2)\\\\\text{x} = (5)/(2)-7 \ \text{ or } \ \text{x} = -(5)/(2)-7\\\\\text{x} = (5)/(2)-(14)/(2) \ \text{ or } \ \text{x} = -(5)/(2)-(14)/(2)\\\\\text{x} = (5-14)/(2) \ \text{ or } \ \text{x} = (-5-14)/(2)\\\\\text{x} = -(9)/(2) \ \text{ or } \ \text{x} = -(19)/(2)\\\\`