Solve |x^2 - 2x - 3| = x

Question

Solve the equation

x_{1} = \frac{1 + 13}{2}, x_{2} = \frac{3 + 21}{2}

Alternative Form

x_{1} \approx 2.302776, x_{2} \approx 3.791288

Evaluate

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

Rewrite the expression

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

Separate the equation into 2 possible cases

x^{2} - 2 x - 3 - x = 0, x^{2} - 2 x - 3 \geq 0 - (x^{2} - 2 x - 3) - x = 0, x^{2} - 2 x - 3 < 0

Solve the equation

More Steps

x = \frac{3 + 21}{2} x = \frac{3 - 21}{2}, x^{2} - 2 x - 3 \geq 0 - (x^{2} - 2 x - 3) - x = 0, x^{2} - 2 x - 3 < 0

Solve the inequality

More Steps

x = \frac{3 + 21}{2} x = \frac{3 - 21}{2}, x \in (- \infty, - 1] \cup [3, + \infty) - (x^{2} - 2 x - 3) - x = 0, x^{2} - 2 x - 3 < 0

Solve the equation

More Steps

x = \frac{3 + 21}{2} x = \frac{3 - 21}{2}, x \in (- \infty, - 1] \cup [3, + \infty) x = \frac{1 + 13}{2} x = \frac{1 - 13}{2}, x^{2} - 2 x - 3 < 0

Solve the inequality

More Steps

x = \frac{3 + 21}{2} x = \frac{3 - 21}{2}, x \in (- \infty, - 1] \cup [3, + \infty) x = \frac{1 + 13}{2} x = \frac{1 - 13}{2}, - 1 < x < 3

Find the intersection

x = \frac{3 + 21}{2} x = \frac{1 + 13}{2} x = \frac{1 - 13}{2}, - 1 < x < 3

Find the intersection

x = \frac{3 + 21}{2} x = \frac{1 + 13}{2}

Solution

x_{1} = \frac{1 + 13}{2}, x_{2} = \frac{3 + 21}{2}

Alternative Form

x_{1} \approx 2.302776, x_{2} \approx 3.791288

Show Solution