Solve 2s^2-s-10 - ScanMath

Question

Factor the expression

(s + 2) (2 s - 5)

Evaluate

2 s^{2} - s - 10

Rewrite the expression

2 s^{2} + (- 5 + 4) s - 10

Calculate

2 s^{2} - 5 s + 4 s - 10

Rewrite the expression

s \times 2 s - s \times 5 + 2 \times 2 s - 2 \times 5

Factor out s from the expression

s (2 s - 5) + 2 \times 2 s - 2 \times 5

Factor out 2 from the expression

s (2 s - 5) + 2 (2 s - 5)

Solution

(s + 2) (2 s - 5)

Show Solution

s_{1} = - 2, s_{2} = \frac{5}{2}

Alternative Form

s_{1} = - 2, s_{2} = 2.5

Evaluate

2 s^{2} - s - 10

To find the roots of the expression,set the expression equal to 0

2 s^{2} - s - 10 = 0

Factor the expression

More Steps

Evaluate

2 s^{2} - s - 10

Rewrite the expression

2 s^{2} + (- 5 + 4) s - 10

Calculate

2 s^{2} - 5 s + 4 s - 10

Rewrite the expression

s \times 2 s - s \times 5 + 2 \times 2 s - 2 \times 5

Factor out s from the expression

s (2 s - 5) + 2 \times 2 s - 2 \times 5

Factor out 2 from the expression

s (2 s - 5) + 2 (2 s - 5)

Factor out 2 s - 5 from the expression

(s + 2) (2 s - 5)

(s + 2) (2 s - 5) = 0

When the product of factors equals 0,at least one factor is 0

s + 2 = 0 2 s - 5 = 0

Solve the equation for s

More Steps

Evaluate

s + 2 = 0

Move the constant to the right-hand side and change its sign

s = 0 - 2

Removing 0 doesn't change the value,so remove it from the expression

s = - 2

s = - 2 2 s - 5 = 0

Solve the equation for s

More Steps

Evaluate

2 s - 5 = 0

Move the constant to the right-hand side and change its sign

2 s = 0 + 5

Removing 0 doesn't change the value,so remove it from the expression

2 s = 5

Divide both sides

\frac{2 s}{2} = \frac{5}{2}

Divide the numbers

s = \frac{5}{2}

s = - 2 s = \frac{5}{2}

Solution

s_{1} = - 2, s_{2} = \frac{5}{2}

Alternative Form

s_{1} = - 2, s_{2} = 2.5

Show Solution