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What is the solution for $x^2+4x>77$

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Evaluate integers raised to positive rational exponents

Full solution

Q. What is the solution for

x^2+4x>77

Subtract $77$ : Step $1$ : Subtract $77$ from both sides of the inequality. $x^2 + 4x - 77 > 0$
Factorize expression: Step $2$ : Factorize the quadratic expression. $\newline$ $x^2 + 4x - 77$ $\newline$ = $(x + 11)(x - 7)$
Find critical points: Step $3$ : Set the factors equal to zero to find critical points. $\newline$ $x + 11 = 0 \rightarrow x = -11$ $\newline$ $x - 7 = 0 \rightarrow x = 7$
Test intervals: Step $4$ : Test the intervals determined by the critical points in the inequality $(x + 11)(x - 7) > 0$ . $\newline$ - Test $x = -12$ : $(-12 + 11)(-12 - 7) = (-1)(-19) = 19 > 0$ $\newline$ - Test $x = 0$ : $(0 + 11)(0 - 7) = 11(-7) = -77 < 0$ $\newline$ - Test $x = 8$ : $(8 + 11)(8 - 7) = 19(1) = 19 > 0$
Write solution: Step $5$ : Write the solution based on the test results. $\newline$ The expression $(x + 11)(x - 7) > 0$ when $x < -11$ or $x > 7$ .

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