Complete question is;
Type the correct answer in each box. Use numerals instead of words. Consider this quadratic equation. x² + 2x + 7 = 21 The number of positive solutions to this equation is . The approximate value of the greatest solution to the equation, rounded to the nearest hundredth, is
Answer:
The approximate value of the greatest solution to the equation, rounded to the nearest hundredth, is 2.87.
Explanation:
We are given the quadratic equation as;
x² + 2x + 7 = 21
Subtract 21 from both sides to give ;
x² + 2x + 7 - 21 = 0
x² + 2x - 14 = 0
Using quadratic formula, we cam find the roots of the equation.
x = [-b ± √b² - 4ac]/2a
Plugging in the values;
x = [-2 ± √(2² - 4(1*-14))]/2(1)
x = [-2 ± √(4 + 56)]/2
x = [-2 ± √60]/2
x = - 4.87 or 2.87
Thus, this equation has only one positive solution which is the greatest.
Thus, greatest solution is 2.87