Question:
If \( 3(x^2 + x) - 7 = x^2 + 2(4 + x^2) \), then \( x = ? \)
If \( 3(x^2 + x) - 7 = x^2 + 2(4 + x^2) \), then \( x = ? \)
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When solving quadratic equations, first expand both sides, simplify, and then solve for the unknown.
Updated On: Oct 3, 2025
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The Correct Option is B
Solution and Explanation
Step 1: Expand and simplify both sides.
On the left-hand side, expand \( 3(x^2 + x) - 7 \): \[ 3(x^2 + x) - 7 = 3x^2 + 3x - 7. \] On the right-hand side, expand \( x^2 + 2(4 + x^2) \): \[ x^2 + 2(4 + x^2) = x^2 + 8 + 2x^2 = 3x^2 + 8. \] Step 2: Set the two expressions equal.
Now we have the equation: \[ 3x^2 + 3x - 7 = 3x^2 + 8. \] Step 3: Solve for \( x \).
Cancel out \( 3x^2 \) from both sides: \[ 3x - 7 = 8. \] Add 7 to both sides: \[ 3x = 15. \] Divide by 3: \[ x = 5. \] Conclusion:
The correct answer is (B) 6.
On the left-hand side, expand \( 3(x^2 + x) - 7 \): \[ 3(x^2 + x) - 7 = 3x^2 + 3x - 7. \] On the right-hand side, expand \( x^2 + 2(4 + x^2) \): \[ x^2 + 2(4 + x^2) = x^2 + 8 + 2x^2 = 3x^2 + 8. \] Step 2: Set the two expressions equal.
Now we have the equation: \[ 3x^2 + 3x - 7 = 3x^2 + 8. \] Step 3: Solve for \( x \).
Cancel out \( 3x^2 \) from both sides: \[ 3x - 7 = 8. \] Add 7 to both sides: \[ 3x = 15. \] Divide by 3: \[ x = 5. \] Conclusion:
The correct answer is (B) 6.
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