Solve 10-x-2x^2 - ScanMath

Question

Factor the expression

(2 - x) (5 + 2 x)

Evaluate

10 - x - 2 x^{2}

Rewrite the expression

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

Calculate

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

Rewrite the expression

2 \times 5 + 2 \times 2 x - x \times 5 - x \times 2 x

Factor out 2 from the expression

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

Factor out - x from the expression

2 (5 + 2 x) - x (5 + 2 x)

Solution

(2 - x) (5 + 2 x)

Show Solution

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

Alternative Form

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

Evaluate

10 - x - 2 x^{2}

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

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

Factor the expression

More Steps

Evaluate

10 - x - 2 x^{2}

Rewrite the expression

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

Calculate

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

Rewrite the expression

2 \times 5 + 2 \times 2 x - x \times 5 - x \times 2 x

Factor out 2 from the expression

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

Factor out - x from the expression

2 (5 + 2 x) - x (5 + 2 x)

Factor out 5 + 2 x from the expression

(2 - x) (5 + 2 x)

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

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

2 - x = 0 5 + 2 x = 0

Solve the equation for x

More Steps

Evaluate

2 - x = 0

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

- x = 0 - 2

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

- x = - 2

Change the signs on both sides of the equation

x = 2

x = 2 5 + 2 x = 0

Solve the equation for x

More Steps

Evaluate

5 + 2 x = 0

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

2 x = 0 - 5

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

2 x = - 5

Divide both sides

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

Divide the numbers

x = \frac{- 5}{2}

Use \frac{- a}{b} = \frac{a}{- b} = - \frac{a}{b} to rewrite the fraction

x = - \frac{5}{2}

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

Solution

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

Alternative Form

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

Show Solution