Use the zero product property to find the solutions to the equation x^2 + x – 30 = 12. x = –7 or x = 6 x = –7 or x = –6 x = –6 or x = 7 x = 6 or x = 7

x2 + x - 30 = 12

x2 + x - 42 = 0

(x + 7)(x - 6) = 0

By zero product property, either (x + 7) = 0 or (x - 6) = 0.

So x = -7/6.

x = - 7 or x = 6

Step-by-step explanation:

given

x² + x - 30 = 12 ( subtract 12 from both sides )

x² + x - 42 = 0 ← in standard form

To factorise, consider the factors of the constant term (- 42) which sum to give the coefficient of the x- term (+ 1)

The factors are + 7 and - 6, since

+ 7 × - 6 = - 42 and + 7 - 6 = + 1, hence

(x + 7)(x - 6) = 0

Equate each factor to zero and solve for x ( zero product property )

x + 7 = 0 ⇒ x = - 7

x - 6 = 0 ⇒ x = 6

x = 25/2304

step-by-step explanation:

1 number

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.