Question:
If twice the square of a number is 45 more than 13 times of it, then what is the cube of that number?
If twice the square of a number is 45 more than 13 times of it, then what is the cube of that number?
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Convert word problems into equations first, then solve step by step.
Updated On: Apr 23, 2026
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The Correct Option is C
Solution and Explanation
Concept:
Form equation using given condition.
Step 1: Let number = $x$.
\[ 2x^2 = 13x + 45 \]
Step 2: Rearrange equation.
\[ 2x^2 - 13x - 45 = 0 \]
Step 3: Factorize.
\[ 2x^2 - 18x + 5x - 45 = 0 \] \[ 2x(x - 9) + 5(x - 9) = 0 \] \[ (2x + 5)(x - 9) = 0 \]
Step 4: Find value of $x$.
\[ x = 9 \quad ({positive value}) \]
Step 5: Find cube.
\[ x^3 = 9^3 = 729 \]
Hence, the cube of the number is 729.
Step 1: Let number = $x$.
\[ 2x^2 = 13x + 45 \]
Step 2: Rearrange equation.
\[ 2x^2 - 13x - 45 = 0 \]
Step 3: Factorize.
\[ 2x^2 - 18x + 5x - 45 = 0 \] \[ 2x(x - 9) + 5(x - 9) = 0 \] \[ (2x + 5)(x - 9) = 0 \]
Step 4: Find value of $x$.
\[ x = 9 \quad ({positive value}) \]
Step 5: Find cube.
\[ x^3 = 9^3 = 729 \]
Hence, the cube of the number is 729.
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