\( x = \frac { - 2 \pm \sqrt { 2 ^ { 2 } - 4 ( 1 ) ( - 15 ) } } { 2 ( 1 ) } \)

Calculate the value by following steps: - step0: Calculate: \(-2+\frac{\sqrt{2^{2}-4\times 1\times \left(-15\right)}}{\left(2\times 1\right)}\) - step1: Remove the parentheses: \(-2+\frac{\sqrt{2^{2}-4\times 1\times \left(-15\right)}}{2\times 1}\) - step2: Multiply the terms: \(-2+\frac{\sqrt{2^{2}+60}}{2\times 1}\) - step3: Add the numbers: \(-2+\frac{\sqrt{64}}{2\times 1}\) - step4: Simplify the root: \(-2+\frac{8}{2\times 1}\) - step5: Reduce the fraction: \(-2+4\) - step6: Add the numbers: \(2\) Calculate or simplify the expression \( -2 - \sqrt(2^2 - 4 * 1 * -15) / (2 * 1) \). Calculate the value by following steps: - step0: Calculate: \(-2-\frac{\sqrt{2^{2}-4\times 1\times \left(-15\right)}}{\left(2\times 1\right)}\) - step1: Remove the parentheses: \(-2-\frac{\sqrt{2^{2}-4\times 1\times \left(-15\right)}}{2\times 1}\) - step2: Multiply the terms: \(-2-\frac{\sqrt{2^{2}+60}}{2\times 1}\) - step3: Add the numbers: \(-2-\frac{\sqrt{64}}{2\times 1}\) - step4: Simplify the root: \(-2-\frac{8}{2\times 1}\) - step5: Reduce the fraction: \(-2-4\) - step6: Subtract the numbers: \(-6\) Para resolver la ecuación cuadrática dada: \[ x = \frac{-2 \pm \sqrt{2^2 - 4(1)(-15)}}{2(1)} \] Primero, calculamos el discriminante: \[ 2^2 - 4(1)(-15) = 4 + 60 = 64 \] Ahora, sustituimos el discriminante en la fórmula: \[ x = \frac{-2 \pm \sqrt{64}}{2} \] Calculamos la raíz cuadrada de 64: \[ \sqrt{64} = 8 \] Ahora tenemos dos soluciones: 1. Para \( x = \frac{-2 + 8}{2} \): \[ x = \frac{6}{2} = 3 \] 2. Para \( x = \frac{-2 - 8}{2} \): \[ x = \frac{-10}{2} = -5 \] Por lo tanto, las soluciones de la ecuación son: \[ x = 3 \quad \text{y} \quad x = -5 \]