How to solve this Olympiad Maths problem 5x^x - 45x = 0

June 29, 2026Mathematics

ScanSolve AI Answer

June 29, 2026

Answer

x=0, x=9

Step 1: Identify the common factor in the equation $5x^2 - 45x = 0$ . Both terms have $5x$ as a common factor. $5x^2 - 45x = 0$

Step 2: Factor out the common factor $5x$ . $5x(x - 9) = 0$

Step 3: For the product of two factors to be zero, at least one of the factors must be zero. Set each factor equal to zero and solve for $x$ . $5x = 0 \quad or \quad x - 9 = 0$

Step 4: Solve the first equation for $x$ . $5x = 0$ $x = \frac{0}{5}$ $x = 0$

Step 5: Solve the second equation for $x$ . $x - 9 = 0$ $x = 9$

The solutions for $x$ are $0$ and $9$ .

The final answer is $\boxed{x=0, x=9}$ .

Drop the next question.

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Quick Answer

Identify the common factor in the equation 5x^2 - 45x = 0. Both terms have 5x as a common factor.

Asked on June 29, 2026Mathematics

This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

ScanSolve AI AnswerAnswered on June 29, 2026

Step 1: Identify the common factor in the equation 5x^2 - 45x = 0. Both terms have 5x as a common factor. 5x^2 - 45x = 0 Step 2: Factor out the common factor 5x. 5x(x - 9) = 0 Step 3: For the product of two factors to be zero, at least one of the factors must be zero. Set each factor equal to zero and solve for x. 5x = 0 or x - 9 = 0 Step 4: Solve the first equation for x. 5x = 0 x = (0)/(5) x = 0 Step 5: Solve the second equation for x. x - 9 = 0 x = 9 The solutions for x are 0 and 9. The final answer is x=0, x=9. Drop the next question.

Asked on June 29, 2026Mathematics

ScanSolve AI AnswerAnswered on June 29, 2026

Step 1: Identify the common factor in the equation 5x^2 - 45x = 0. Both terms have 5x as a common factor. 5x^2 - 45x = 0 Step 2: Factor out the common factor 5x. 5x(x - 9) = 0 Step 3: For the product of two factors to be zero, at least one of the factors must be zero. Set each factor equal to zero and solve for x. 5x = 0 or x - 9 = 0 Step 4: Solve the first equation for x. 5x = 0 x = (0)/(5) x = 0 Step 5: Solve the second equation for x. x - 9 = 0 x = 9 The solutions for x are 0 and 9. The final answer is x=0, x=9. Drop the next question.