Questions: Solve: (x^2+3x-4=0)

Transcript text: Solve: $x^{2}+3 x-4=0$

Solution

Solution Steps

To solve the quadratic equation $x^2 + 3x - 4 = 0$, we can use the quadratic formula $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$, where $a$, $b$, and $c$ are the coefficients from the equation $ax^2 + bx + c = 0$.

Step 1: Identify Coefficients

For the quadratic equation $x^2 + 3x - 4 = 0$, we identify the coefficients:

$a = 1$
$b = 3$
$c = -4$

Step 2: Calculate the Discriminant

The discriminant $D$ is calculated using the formula: \[ D = b^2 - 4ac \] Substituting the values: \[ D = 3^2 - 4 \cdot 1 \cdot (-4) = 9 + 16 = 25 \]

Step 3: Apply the Quadratic Formula

Using the quadratic formula: \[ x = \frac{-b \pm \sqrt{D}}{2a} \] we find the two solutions: \[ x_1 = \frac{-3 + \sqrt{25}}{2 \cdot 1} = \frac{-3 + 5}{2} = \frac{2}{2} = 1 \] \[ x_2 = \frac{-3 - \sqrt{25}}{2 \cdot 1} = \frac{-3 - 5}{2} = \frac{-8}{2} = -4 \]

Final Answer

The solutions to the equation are: \[ \boxed{x_1 = 1} \quad \text{and} \quad \boxed{x_2 = -4} \]

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