what is the answer in algebraic notation?
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By adding 4x to both sides, we have:
x^2 - 5 ≤ -4x ==> x^2 + 4x - 5 ≤ 0.
Then, by factoring:
x^2 + 4x - 5 ≤ 0 ==> (x + 5)(x - 1) ≤ 0.
Now, a quadratic equation with a positive leading coefficient is negative in-between its two roots (take a look at the graph of some to see why). Since the roots of (x + 5)(x - 1) are x = -5 and x = 1, we see that the solution is -5 ≤ x ≤ 1.
I hope this helps!
x^2 - 5 ≤ -4x ==> x^2 + 4x - 5 ≤ 0.
Then, by factoring:
x^2 + 4x - 5 ≤ 0 ==> (x + 5)(x - 1) ≤ 0.
Now, a quadratic equation with a positive leading coefficient is negative in-between its two roots (take a look at the graph of some to see why). Since the roots of (x + 5)(x - 1) are x = -5 and x = 1, we see that the solution is -5 ≤ x ≤ 1.
I hope this helps!
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x² - 5 ≤ -4x
x² ≤ -4x + 5
x² + 4x - 5 ≤ 0
(x + 5)(x - 1) ≤ 0
-5 ≤ x ≤ 1
x² ≤ -4x + 5
x² + 4x - 5 ≤ 0
(x + 5)(x - 1) ≤ 0
-5 ≤ x ≤ 1