Solve the quadratic equation x2=25/36.
The question is asking you to solve for x (that is the place the quadratic passes the x-axis) It will pass in two places.
Take the square root of both sides and you see your answer is + and - 5/6 thus the quaratic crosses the x-axis at -5/6, and + 5/6
To solve the quadratic equation x^2 = 25/36, we need to find the values of x that satisfy this equation.
Step 1: Rewrite the equation in standard quadratic form by moving all terms to one side of the equation:
x^2 - 25/36 = 0
Step 2: To solve this equation, we can either factor it or use the quadratic formula. In this case, factoring is not straightforward, so let's use the quadratic formula:
x = (-b ± √(b^2 - 4ac))/(2a)
For our equation, a = 1, b = 0, and c = -25/36. Plugging these values into the quadratic formula, we get:
x = (0 ± √(0^2 - 4(1)(-25/36)))/(2(1))
Step 3: Simplify the expression inside the square root:
x = ± √(0 + 100/36)/2
Step 4: Further simplify the expression:
x = ± √(100/36)/2
x = ± √(100)/√(36)/2
Step 5: Simplify the square roots:
x = ±(10/6)/2
x = ±10/12
Step 6: Simplify the fraction:
x = ±5/6
Therefore, the solutions to the quadratic equation x^2 = 25/36 are x = 5/6 and x = -5/6.