Reviewed by Janice S. Armas
What is the solution(s) to the quadratic equation 9x² = 4?
Answer: The solutions to 9x² = 4 are x = 2/3 and x = -2/3
Quadratic equations like 9x² = 4 are equations where the highest exponent of the variable is 2. Solving such equations usually involves rearranging the equation and using algebraic techniques such as square roots, factoring, or the quadratic formula. In this case, the equation can be solved straightforwardly by isolating x² and taking the square root.
Methods
Math Tutor Explanation Using the Square Root Method
This method involves isolating the x² term and taking the square root of both sides to find the values of x.
Step 1: Step 1: Divide both sides by 9 to get x² = 4/9
Step 2: Step 2: Take the square root of both sides: x = ±√(4/9)
Math Tutor Explanation Using the Quadratic Formula
The quadratic formula can solve any equation in the form ax² + bx + c = 0. Rewrite the original equation and solve for x.
Step 1: Step 1: Rewrite as 9x² - 4 = 0 (so a = 9, b = 0, c = -4)
Step 2: Step 2: Apply the formula: x = [-b ± √(b² - 4ac)] / (2a)
Step 1:
Step 2:
Math Tutor suggests: Practice More Quadratic Equations
Deepen your understanding of solving quadratic equations and related algebra concepts with these additional exercises.
FAQ on Solving Quadratic Equations
What does it mean if a quadratic has no real solution?
It means that the solutions are complex numbers and cannot be represented as real numbers.
Can all quadratic equations be solved using the square root method?
The square root method works best when the equation can be written as x² = number, but not for all forms.
What is the quadratic formula?
The quadratic formula is x = [-b ± √(b² - 4ac)] / (2a) for equations in the form ax² + bx + c = 0.
Why do we write ± when taking a square root?
Because both the positive and negative values squared will yield the same result, so both are valid solutions.
How can I check my solutions?
Substitute the values of x back into the original equation and check if both sides are equal.
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