# Solve: `9p^2 + 8 = -77` 9p^2+8=-77 Solve the equation by taking square roots.

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Please note that I have only now seen the negative:

`9p^2 + 8 = -77`

`9p^2 = -77-8`

`9p^2=-85`

`p^2= (-85)/9`

`sqrtp^2=sqrt(-85/9)`

This would render no solution unless we use imaginary numbers (i):

`therefore p = sqrt9.44 i` or `p=-sqrt9.44 i`

Step # 01: Simplify 9p

2

+8 - -77 //------------ Equation at the end of step 01 : 9p2

+ 85 = 0 //------------ // Step # 02: Solve 9p2

+85 = 0 //------------ # 02.01 Solve : 9p2+85 = 0 Subtract 85 from both sides of the equation: 9p2 = -85 Divide both sides of the equation by 9: p2 = -(85/9) When two things are equal, their square roots are equal. Taking the square root of the two sides of the equation we get: p = ± √ -(85/9) In Math, i is called the imaginary unit. It satisfies i2 = -1 Both i and -i are the square roots of -1 Accordingly, √ -(85/9) = √ -1•(85/9) = √ -1 •√ (85/9) = i • √ (85/9) The equation has no real solutions. It has 2 imaginary, or complex solutions. p = 0.0000 + 3.0732 i p = 0.0000 - 3.0732 i //------------ // Solutions : Two solutions were found //------------ p = 0.0000 - 3.0732 i p = 0.0000 + 3.0732 i**Sources:**