Answer: [B]: Two (2) real solutions . __________________________________________________________ Explanation: __________________________________________________________ Given: -7x² − 11x − 2 = 0 ; __________________________________________________________ We see that it is in "quadratic format" ; that is: __________________________________________________________ " ax² + bx + c = 0 ; a ≠ 0 ; " __________________________________________________________ Multiply the entire equation by "-1" ; to get rid of the "negative number" : __________________________________________________________ → -1 * {-7x² − 11x − 2 = 0} ; __________________________________________________________ to get: → 7x² + 11x + 2 = 0 ; __________________________________________________________ This expression is written in the "quadratic format";
ax² + bx + c = 0 ; in which: a = 7 ; b = 11; c = 2 ; __________________________________________________________ The expression cannot be "factored"; so, we can solve for "x" ; by using the "quadratic equation formula" ; __________________________________________________________
x = {-b ± √(b² − 4ac)} / {2a} ; ______________________________________ Let us solve for: "(2a)" : 2a = 2 * a = 2 * 7 = 14 ;
Let us solve for: "(b² − 4ac)": 11² − 4*7*2 = 121 − 56 = 65;
→ √(b² − 4ac) = √65 ______________________________________ → " -b" = -11 ; ________________________________________________ So, x = (-11 ± √65) / 14 ; ________________________________________________ There are TWO (2) solutions: _______________________________________________________ Solution 1) x = (-11 + √65) / 14 = - 0.2098387322643893071; AND: _______________________________________________________ Solution 2) x = (-11 − √65) / 14 = -1.3615898391641821214 ; _______________________________________________________ So, there are TWO (2) real solutions. _______________________________________________________
