Final answer:
To solve the equation x(5x+4)=1, expand it to the standard quadratic form 5x^2 + 4x - 1 = 0 and then apply the quadratic formula to find the possible values for x.
Step-by-step explanation:
To solve the equation x(5x+4)=1, we must first expand the equation to its standard quadratic form by distributing the x across the terms in the parentheses. The expanded equation becomes 5x^2 + 4x - 1 = 0. At this point, we have a quadratic equation in the form of ax^2 + bx + c = 0. Although this equation does not seem to have easily factorable numbers, the quadratic formula can be used to find x.
The quadratic formula is x = (-b ± √(b^2-4ac))/(2a), where a, b, and c are coefficients from the quadratic equation ax^2 + bx + c = 0. Substituting our coefficients (a=5, b=4, and c=-1) into the formula, we get two potential solutions for x.
After calculating these values, the student will have the two possible values for x that satisfy the original equation.