What are the solutions to the quadratic equation below?
4X2 +28x + 49 = 5

4* 2 + 28x + 49 = 5
8 + 28x + 49 = 5
28 + 57 = 5
- 57 -57
———————————
28x = - 52
———————-
28x = 28

x = - 13/7

1) Multiple the numbers
2) Add the numbers
3) Add the same terms to both sides of the equation
4) Simplify
5) Divide both sides of the equation
6) Simplify

Answer

1 number

explanation

if we use a graphing calculator, there is only one such number that satisfies the conclusion of the mean value theorem, that is, a number such that

 

where the right-hand side is the average rate of change of f on the interval [0.5,0.75], which is the slope of the secant line.

in the attached graph, the black line is the secant line which has its slope as the average rate of change of f on [0.5,0.75], while the orange line is the only tangent line to the graph of f in the interval that satisfies the mvt conclusion.

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