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MATH / Sviatoslav solved the quadratic equation x²−x−1=0 by completing the square. In the process, he came up with the equivalent equation (x+a)²=b,where a and b are constants. What is b?

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problem

Sviatoslav solved the quadratic equation x2−x−1=0x^2-x-1=0 by completing the square. In the process, he came up with the equivalent equation (x+a)2=b,(x+a)^2 = b,where aa and bb are constants. What is bb?
Plain-text mathematical notation (without MathML)
Sviatoslav solved the quadratic equation x²−x−1=0 by completing the square. In the process, he came up with the equivalent equation (x+a)²=b,where a and b are constants.

What is b?
Original LaTeX notation
Sviatoslav solved the quadratic equation $x^2-x-1=0$ by completing the square. In the process, he came up with the equivalent equation $$(x+a)^2 = b,$$where $a$ and $b$ are constants.

What is $b$?

level

Level 4

type

Algebra

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Source and history

task_id
b0e0eac8-05c5-5398-b013-0d9f391e7294
task_key
algebra--test--b0e0eac8-05c5-5398-b013-0d9f391e7294
task_revision_id
1
config / split
algebra / test

Official source

initial import