Question

In using the quadratic formula to solve for the equation x² + 14x - 46 = 0, the solution would be where -b = -14 and d = 332.

Answer 1

The solutions to the quadratic equation x² + 14x - 46 = 0 are x = -7 + √95 and x = -7 - √95.

Step-by-step explanation:

The given equation x² + 14x - 46 = 0 is a quadratic equation of the form ax² + bx + c = 0, with a = 1, b = 14, and c = -46. To solve this equation using the quadratic formula, we substitute these values into the formula:

x = (-b ± √(b² - 4ac)) / (2a)

Substituting the values, we get:

x = (-14 ± √(14² - 4*1*(-46))) / (2*1)

x = (-14 ± √(196 + 184)) / 2

x = (-14 ± √380) / 2

Now, calculating the square root of 380 and simplifying the expression, we have:

x = (-14 ± √(4 * 95)) / 2

x = (-14 ± 2√95) / 2

Simplifying further, we get:

x = -7 ± √95

So, the solutions to the quadratic equation x² + 14x - 46 = 0 are x = -7 + √95 and x = -7 - √95.