Solve x: x^2 - 3x - 10 = 0

Question

Solve the equation

x_{1} = - \frac{5 + 2 7}{3}, x_{2} = \frac{- 5 + 2 7}{3}

Alternative Form

x_{1} \approx - 3.430501, x_{2} \approx 0.097168

Evaluate

x \div x^{2} - 3 x - 10 = 0

Find the domain

More Steps

x \div x^{2} - 3 x - 10 = 0, x \neq = 0

Divide the terms

More Steps

\frac{1}{x} - 3 x - 10 = 0

Multiply both sides of the equation by LCD

(\frac{1}{x} - 3 x - 10) x = 0 \times x

Simplify the equation

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1 - 3 x^{2} - 10 x = 0 \times x

Any expression multiplied by 0 equals 0

1 - 3 x^{2} - 10 x = 0

Rewrite in standard form

- 3 x^{2} - 10 x + 1 = 0

Multiply both sides

3 x^{2} + 10 x - 1 = 0

Substitute a= 3,b= 10 and c= - 1 into the quadratic formula x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

x = \frac{- 10 \pm 1 0 ^{2} - 4 \times 3 ( - 1 )}{2 \times 3}

Simplify the expression

x = \frac{- 10 \pm 1 0 ^{2} - 4 \times 3 ( - 1 )}{6}

Simplify the expression

More Steps

x = \frac{- 10 \pm 112}{6}

Simplify the radical expression

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x = \frac{- 10 \pm 4 7}{6}

Separate the equation into 2 possible cases

x = \frac{- 10 + 4 7}{6} x = \frac{- 10 - 4 7}{6}

Simplify the expression

More Steps

x = \frac{- 5 + 2 7}{3} x = \frac{- 10 - 4 7}{6}

Simplify the expression

More Steps

x = \frac{- 5 + 2 7}{3} x = - \frac{5 + 2 7}{3}

Check if the solution is in the defined range

x = \frac{- 5 + 2 7}{3} x = - \frac{5 + 2 7}{3}, x \neq = 0

Find the intersection of the solution and the defined range

x = \frac{- 5 + 2 7}{3} x = - \frac{5 + 2 7}{3}

Solution

x_{1} = - \frac{5 + 2 7}{3}, x_{2} = \frac{- 5 + 2 7}{3}

Alternative Form

x_{1} \approx - 3.430501, x_{2} \approx 0.097168

Show Solution