Solve each equation by completing the square. a) x2+16x+45=−10

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Solve each equation by completing the square.  a) x2+16x+45=−10

maul124uk · Accepted Answer

Step 1  We have,  x2+16x+45=−10  By the method of completing square we have,  x2+16x+(8)2−(8)2+45=−10  (x+8)2=−10−45+64  (x+8)2=−55+64  (x+8)2=9  x+8=9  x+8=±3  x=±3−8  either x=3−8 or x=−3−8  either x=−5 or x=−11  We have,  b2−4ac=(16)2−4×1×55  =256−220  =36  Since b2−4ac&amp;gt;0  Therefore the given equation has two distinct real roots.  Step 2

Laura Worden · Accepted Answer

Step 1  x2+16x+45=−10  The form: ax2+bx+c=0 the quadratic formula: −b±b2−4ac2a  Add 10 to both sides of the equation.  x2+16x+45−(−10)=−10−(−10)  Subtracting -10 from itself leaves 0.  x2+16x+55=0  Substitute 1 for a, 16 for b, and 55 for c n the quadratic formula, −b±b2−4ac2a  x=−16±162−4×552  Square 16  x=−16±256−4×552  Multiply -4 times 55  x=−16±256−2202  Add 256 to -220  x=−16±362  Take the square root of 36  x=−16±62  Now solve the equation when ± is plus and minus  Add -16 to 6  x=−102  Divide -10 by 2  x=−5  Subtract 6 from -16  x=−222  Divide -22 by 2  x=−11

Solve each equation by completing the square. a) x^{2}+16x+45=-10

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