To solve the quadratic equation x^2 + 4x - 7 = 0, you can use the quadratic formula:
1. Identify the coefficients of the quadratic equation: a = 1 (coefficient of x^2), b = 4 (coefficient of x), and c = -7 (constant term).
2. Plug the values of a, b, and c into the quadratic formula: x = [-b ± √(b^2 - 4ac)] / 2a
3. Substitute the values into the formula: x = [-4 ± √(4^2 - 4*1*(-7))] / 2*1
4. Simplify the equation: x = [-4 ± √(16 + 28)] / 2
5. Further simplify: x = [-4 ± √44] / 2
6. Calculate the square root of 44: √44 = 2√11
7. Substitute the simplified value back into the equation: x = [-4 ± 2√11] / 2
8. Split the equation into two solutions (using the ± sign): x = (-4 + 2√11) / 2 and x = (-4 - 2√11) / 2
9. Simplify each solution: x = (-4 + 2√11) / 2 simplifies to x = -2 + √11 and x = (-4 - 2√11) / 2 simplifies to x = -2 - √11
Therefore, the solutions to the quadratic equation x^2 + 4x - 7 = 0 are x = -2 + √11 and x = -2 - √11.
