The solution to x^2-6x<=-7 is -sqrt(2)+3<= x<= sqrt(2)+3

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x^2-6x<=-7

Solution

x^{2} - 6 x \leq - 7

- 2 + 3 \leq x \leq 2 + 3

Interval Notation

[- 2 + 3, 2 + 3]

Decimal Notation

1.58578 \dots \leq x \leq 4.41421 \dots

Solution steps

x^{2} - 6 x \leq - 7

Rewrite in standard form

x^{2} - 6 x + 7 \leq 0

Complete the square

x^{2} - 6 x + 7 : (x - 3)^{2} - 2

(x - 3)^{2} - 2 \leq 0

Move

2

to the right side

(x - 3)^{2} \leq 2

For

u^{n} \leq a

, if

n

is even then

- 2 \leq x - 3 \leq 2

a \leq u \leq b

then

a \leq u and u \leq b

- 2 \leq x - 3 and x - 3 \leq 2

- 2 \leq x - 3 : x \geq - 2 + 3

x - 3 \leq 2 : x \leq 2 + 3

Combine the intervals

x \geq - 2 + 3 and x \leq 2 + 3

Merge Overlapping Intervals

- 2 + 3 \leq x \leq 2 + 3

- 108 = 2 (6 n - 6)

(1 + \frac{0.12}{2})^{2} - 1

(x - 4) (x + 2)^{2} < 0

x^{2} + 4 x - 40 = - 8

\frac{240 π}{180}