Question

Use a calculator and the quadratic formul: 6.99x² +2.65x=5.26

Answer 1

Using the quadratic formula, the solutions for the equation 6.99x² + 2.65x = 5.26 are x = -1 and x ≈ 0.608.

Explanation:

The quadratic formula,
`\(x = (-b \pm √(b^2 - 4ac))/(2a)\)`, helps find the roots of a quadratic equation in the form ax² + bx + c = 0. In the provided equation 6.99x² + 2.65x = 5.26, we rearrange the terms to bring it into the standard quadratic form ax² + bx + c = 0 by subtracting 5.26 from both sides, resulting in 6.99x² + 2.65x - 5.26 = 0. Here, a = 6.99, b = 2.65, and c = -5.26.

Applying the quadratic formula with the coefficients a, b, and c from the equation, we substitute these values into the formula. First, calculate the discriminant (b² - 4ac) under the square root. Then, use the quadratic formula to find the values of x. The formula yields two solutions due to the pm sign, which are the values of x that satisfy the equation.

Upon computation, the solutions are x = -1 and x ≈ 0.608. These values represent the points where the quadratic equation intersects the x-axis, denoting the values of x that satisfy the original equation. Therefore, utilizing the quadratic formula aids in determining the roots of the quadratic equation and finding the values of x that make the equation true.