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(x+10)(x-4)=0

2 min read Jun 16, 2024
(x+10)(x-4)=0

Solving the Equation (x + 10)(x - 4) = 0

This equation is a quadratic equation in factored form. To find the solutions, we can use the Zero Product Property, which states that if the product of two factors is zero, then at least one of the factors must be zero.

Here's how to solve the equation:

  1. Set each factor equal to zero:

    • x + 10 = 0
    • x - 4 = 0

  2. Solve for x in each equation:

    • x = -10
    • x = 4

Therefore, the solutions to the equation (x + 10)(x - 4) = 0 are x = -10 and x = 4.

Understanding the Solutions

These solutions represent the x-intercepts of the parabola that the equation represents. The parabola intersects the x-axis at the points (-10, 0) and (4, 0).

Checking the Solutions

We can verify our solutions by plugging them back into the original equation:

  • For x = -10:
    • (-10 + 10)(-10 - 4) = (0)(-14) = 0
  • For x = 4:
    • (4 + 10)(4 - 4) = (14)(0) = 0

Since both solutions satisfy the original equation, we have confirmed their validity.

Conclusion

By applying the Zero Product Property, we successfully solved the quadratic equation (x + 10)(x - 4) = 0 and found the solutions x = -10 and x = 4. These solutions represent the x-intercepts of the parabola represented by the equation.

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