question solution

x^{2} - x - 5 \geq x - 2

Rearrange the terms

Rearrange all nonzero terms to the left side of the equation

x^{2} - x - 5 - x + 2 \geq 0

x^{2} - x - 5 - x + 2 \geq 0

Combine like terms

x^{2} - 2 x - 3 \geq 0

x^{2} - 2 x - 3 \geq 0

Convert inequality to equation

x^{2} - 2 x - 3 = 0

x^{2} - 2 x - 3 = 0

Identify the coefficients

a = 1, b = - 2, c = - 3

a = 1, b = - 2, c = - 3

Use the quadratic formula

Substitute into

x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

x = \frac{- ( - 2 ) + ( - 2 ) ^{2} - 4 \times ( - 3 )}{2}

or

x = \frac{- ( - 2 ) - ( - 2 ) ^{2} - 4 \times ( - 3 )}{2}

x = \frac{- ( - 2 ) + ( - 2 ) ^{2} - 4 \times ( - 3 )}{2}

or

x = \frac{- ( - 2 ) - ( - 2 ) ^{2} - 4 \times ( - 3 )}{2}

More steps

Show more steps

x = \frac{- ( - 2 ) + ( - 2 ) ^{2} - 4 \times ( - 3 )}{2}

Determine the sign

x = \frac{2 + 2 ^{2} + 4 \times 3}{2}

Calculate the power

x = \frac{2 + 4 + 4 \times 3}{2}

Calculate the product or quotient

x = \frac{2 + 4 + 12}{2}

Calculate the sum or difference

x = \frac{2 + 16}{2}

Factor and rewrite the radicand in exponential form

x = \frac{2 + 4}{2}

Calculate the sum or difference

x = \frac{6}{2}

Cross out the common factor

x = 3

Cross out the common factor

x = 3

x = \frac{- ( - 2 ) - ( - 2 ) ^{2} - 4 \times ( - 3 )}{2}

Determine the sign

x = \frac{2 - 2 ^{2} + 4 \times 3}{2}

Calculate the power

x = \frac{2 - 4 + 4 \times 3}{2}

Calculate the product or quotient

x = \frac{2 - 4 + 12}{2}

Calculate the sum or difference

x = \frac{2 - 16}{2}

Factor and rewrite the radicand in exponential form

x = \frac{2 - 4}{2}

Calculate the sum or difference

x = \frac{- 2}{2}

Cross out the common factor

x = - 1

Cross out the common factor

x = - 1

x = 3

or

x = - 1

Find the union

Find the union of the solutions

x = 3

or

x = - 1

x = 3

or

x = - 1

Plot

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Find the solution from the graph

Based on the given graph, find the solution of inequality

x \leq - 1

or

x \geq 3

x \leq - 1

or

x \geq 3