Solve for x: a) (x+1)2=16 b) (3x−1)2=0 c) (x+8)2=−9

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Solve for x:  a) (x+1)2=16  b) (3x−1)2=0  c) (x+8)2=−9

lovagwb · Accepted Answer

Step 1  a) (x+1)2=16  ⇒(x+1)=±4  ∴x=3, −5  ∴ No of solutions is 2  Step 2  b) (3x−1)2=0  ∴x=13  No of solutions =1  c) (x+8)2=−9  ⇒x+8−−9  ⇒x=±3i−8  x=3i−8, −3i−8  Here no real solution exist for x.

raefx88y · Accepted Answer

Step 1  a) Given: (x+1)2=16  Take the square root of both sides of the equation.  (x+1)2=16  Simplify.  x+1=4  x+1=−4  Subtract 1 from both sides of the equation.  x=3  x=−5  Step 2  b) Given: (3x−1)2=0  Use binomial theorem (a−b)2=a2−2ab+b2 to expand (3x−1)2  9x2−6x+1=0  This equation is in standard form: ax2+bx+c=0 NSk Substitute 9 for a, -6 for b, and 1 for c in the quadratic formula −b±b2−4ac2a  x=−(−6)±(−6)2−4×92×9  Square -6.  x=−(−6)±36−4×92×9  Multiply -4 times 9.  x=−(−6)±36−362×9  Add 36 to -36.  x=−(−6)±02×9  Take the square root of 0.  x=−62×9  The opposite of -6 is 6.  x=62×9  Multiply 2 times 9.  x=618  Reduce the fraction 618 to lowest terms by extracting and canceling out 6.  x=13  Step 3  c) Given: (x+8)2=−9  Subtract 8 from both sides of the equation.  x+8−8=3i−8  x+8−8=−3i−8  Subtracting 8 from itself leaves 0.  x=3i−8  x=−3i−8  Subtract 8 from 3i.  x=−8+3i  Subtract 8 from -3i.  x=−8−3i  The equation is now solved.  x=−8+3i  x=−8−3i

Solve for x: a) (x+1)^{2}=16 b) (3x-1)^{2}=0 c) (x+8)^{2}=-9

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