(i) $$ 3 x^{2}-4 x=-4 x+5 $$

To solve the quadratic equation: \[ 3x^{2} - 4x = -4x + 5 \] **Step 1:** Simplify the equation by eliminating like terms. Notice that $$-4x$$ appears on both sides of the equation. You can add $$4x$$ to both sides to eliminate these terms: \[ 3x^{2} - 4x + 4x = -4x + 4x + 5 \] \[ 3x^{2} = 5 \] **Step 2:** Solve for $$x^{2}$$. \[ 3x^{2} = 5 \] Divide both sides by 3: \[ x^{2} = \frac{5}{3} \] **Step 3:** Take the square root of both sides to solve for $$x$$. \[ x = \pm \sqrt{\frac{5}{3}} \] **Step 4:** Simplify the square root (optional). Rationalize the denominator: \[ x = \pm \frac{\sqrt{15}}{3} \] **Final Answer:** \[ x = \frac{\sqrt{15}}{3} \quad \text{or} \quad x = -\frac{\sqrt{15}}{3} \] $$ x = \frac{\sqrt{15}}{3} $$ or $$ x = -\frac{\sqrt{15}}{3} $$

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Home Question Bank Math Algebra

Question

(i)

Ask by Lynch Bond. in India

Jan 09,2025

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Bonus Knowledge

To solve the equation

, first, we can simplify it by combining like terms. Adding

to both sides gives us

, which simplifies to

. Next, divide both sides by 3 to isolate

. Now, taking the square root of both sides gives us

or simplifying further

For a quick check on your solution, plug the values of

and

back into the original equation. This not only verifies your solutions but also helps solidify your understanding of why they work. It’s a great way to catch any potential mistakes along the way!

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