Question

Solve the quadratic function of x² 2x-35=0

Answer 1

The quadratic equation x² + 2x - 35 = 0 can be factored into (x + 7)(x - 5) = 0, yielding solutions of x = -7 and x = 5.

Step-by-step explanation:

Solving a Quadratic Equation

To solve the quadratic equation x² + 2x - 35 = 0, we look for two numbers that multiply to -35 and add up to 2. After examining factors of -35, we can see that 7 and -5 meet these criteria. Therefore, we can factor the quadratic equation as (x + 7)(x - 5) = 0. By setting each factor equal to zero, we get x = -7 and x = 5.

We can check our work by plugging these values back into the original equation to ensure that they satisfy the equation.

Indeed, both (-7)² + 2(-7) - 35 = 49 - 14 - 35 = 0 and (5)² + 2(5) - 35 = 25 + 10 - 35 = 0 hold true, confirming that x = -7 and x = 5 are the correct solutions.Therefore, the equation factors as (x - 5)(x + 7) = 0. Solving for x, we get x = 5 and x = -7.

Answer 2

The solutions to the quadratic equation x² + 2x - 35 = 0 are x = 5 and x = -7.

Step-by-step explanation:

To solve the quadratic equation, we can use the quadratic formula x = (-b ± √(b² - 4ac)) / (2a), where a, b, and c are the coefficients of the quadratic equation ax² + bx + c = 0. In this case, the coefficients are a = 1, b = 2, and c = -35. Substituting these values into the quadratic formula, we get x = (-2 ± √164) / 2, which simplifies to x = -1 ± √41. This yields the two solutions x = 5 and x = -7.

The factorization method can also be used to solve the quadratic equation. Factoring x² + 2x - 35 = 0 into (x - 5)(x + 7) = 0 reveals the roots x = 5 and x = -7. This method is straightforward when the quadratic expression can be factored easily.

In conclusion, the quadratic equation x² + 2x - 35 = 0 has solutions x = 5 and x = -7, determined through the quadratic formula and confirmed by factoring. These methods showcase different approaches to solving quadratic equations, providing flexibility in choosing the most suitable method based on the complexity of the equation.