Question

Solve for x. √10−13x=x−4

x=−2 or x=−3
x = 2 or x = 3
no solution
x=−6 or x = 1

Answer 1

To solve the quadratic equation provided by the student, the quadratic formula is used with coefficients a, b, and c. Upon calculation, two solutions are obtained: -0.0024 and 0.00139. However, only the positive value x = 0.00139 is considered a valid solution for real-life contexts.

Step-by-step explanation:

The student's question involves solving a quadratic equation. In mathematics, particularly in algebra, quadratic equations are equations of the second degree, usually in the form of ax² + bx + c = 0, where a, b, and c are coefficients and x represents an unknown. Solving these equations involves finding the values of x that satisfy the equation.

Use the Quadratic Formula

To solve a quadratic equation, one can use the quadratic formula, which states that for any quadratic equation, the values of x can be found using the formula:

x = √(b² - 4ac)/2a

Substituting the given coefficients a = 3, b = 13, and c = -10 into the formula, we get:

x = √(13² - 4 × 3 × (-10))/(2 × 3)

Upon further simplification, we obtain two possible solutions for x: -0.0024 and 0.00139. However, when dealing with measurements or certain real-life situations, negative values may not be feasible, leaving us with x = 0.00139 as the valid solution.