Question

solve x²-8x-1=0 by quadratic formula​

Answer 1

Answer:

$x2−8x−1=0x2-8x-1=0</p><p></p><p> Use the quadratic formula to find the solutions.</p><p></p><p>−b±√b2−4(ac)2a-b±b2-4(ac)2a</p><p></p><p>Substitute the values a=1a=1, b=−8b=-8, and c=−1c=-1 into the quadratic formula and solve for xx.</p><p></p><p>8±√(−8)2−4⋅(1⋅−1)2⋅18±(-8)2-4⋅(1⋅-1)2⋅1</p><p></p><p>Simplify.</p><p></p><p>Tap for more steps...</p><p></p><p>x=4±√17x=4±17</p><p></p><p>The result can be shown in multiple forms.</p><p></p><p>Exact Form:</p><p></p><p>x=4±√17x=4±17</p><p></p><p>Decimal Form:</p><p></p><p>x=8.12310562…,−0.12310562…x=8.12310562…,-0.12310562…</p><p></p><p></p><p>$

Step-by-step explanation:

$In x2+8x+1=0, we observe that coefficient of x is 8 and hence, we can complete the square by adding square of half of 8 i.e. 42=16.</p><p></p><p>Hence x2+8x+1=0 can be written as x2+8x+16−16+1=0 or</p><p></p><p>(x+4)2−15=0 which can be written as</p><p></p><p>(x+4)2−(√15)2=0</p><p></p><p>Now using identity a2−b2=(a+b)(a−b), this can be written as</p><p></p><p>(x+4+√15)(x+4−√15)=0</p><p></p><p>Hence either x+4+√15=0 i.e. x=−4−√15</p><p></p><p>or x+4−√15=0 i.e. x=−4+√15</p><p></p><p>$