Solve 10x^2+21x-10=0

Question

Solve the quadratic equation

Solve by factoring

Solve using the quadratic formula

Solve by completing the square

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

Alternative Form

x_{1} = - 2.5, x_{2} = 0.4

Evaluate

10 x^{2} + 21 x - 10 = 0

Factor the expression

More Steps

Evaluate

10 x^{2} + 21 x - 10

Rewrite the expression

10 x^{2} + (- 4 + 25) x - 10

Calculate

10 x^{2} - 4 x + 25 x - 10

Rewrite the expression

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

Factor out 2 x from the expression

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

Factor out 5 from the expression

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

Factor out 5 x - 2 from the expression

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

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

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

5 x - 2 = 0 2 x + 5 = 0

Solve the equation for x

More Steps

Evaluate

5 x - 2 = 0

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

5 x = 0 + 2

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

5 x = 2

Divide both sides

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

Divide the numbers

x = \frac{2}{5}

x = \frac{2}{5} 2 x + 5 = 0

Solve the equation for x

More Steps

Evaluate

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

Solution

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

Alternative Form

x_{1} = - 2.5, x_{2} = 0.4

Show Solution