What is (x-1)^2-(x+2)^2+3x^2<=-7x+1 ?

The solution to (x-1)^2-(x+2)^2+3x^2<=-7x+1 is -4/3 <= x<= 1

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(x-1)^2-(x+2)^2+3x^2<=-7x+1

(x - 1)^{2} - (x + 2)^{2} + 3 x^{2} \leq - 7 x + 1

- \frac{4}{3} \leq x \leq 1

Interval Notation

[- \frac{4}{3}, 1]

Decimal Notation

- 1.33333 \dots \leq x \leq 1

Solution steps

(x - 1)^{2} - (x + 2)^{2} + 3 x^{2} \leq - 7 x + 1

Rewrite in standard form

3 x^{2} + x - 4 \leq 0

Factor

3 x^{2} + x - 4 : (x - 1) (3 x + 4)

(x - 1) (3 x + 4) \leq 0

Identify the intervals

- \frac{4}{3} \leq x \leq 1

\frac{1 5 ^{4}}{15}

x > 0.05 + 0.9 x

(\frac{8}{3})^{0} \cdot 2^{- 1}

3 x + 5 = 4 x - 4

\frac{x - 2}{4} + \frac{3 x + 2}{6}

What is (x-1)^2-(x+2)^2+3x^2<=-7x+1 ?
The solution to (x-1)^2-(x+2)^2+3x^2<=-7x+1 is -4/3 <= x<= 1