To complete the square, take half of the coefficient of \(j\), which is 18, and square it:
\[\left ( \frac { 18} { 2} \right ) ^ 2 = 9^ 2 = 81.\]

Supplemental Knowledge

Completing the square is a method used to transform a quadratic expression into a perfect-square trinomial. This technique is particularly useful for solving quadratic equations, graphing parabolas, and integrating certain functions in calculus.
To complete the square for a quadratic expression of the form \(j^ 2 + bj\), you need to add and subtract \(( b/2) ^ 2\). This process creates a perfect-square trinomial, which can be factored into \(( j + b/2) ^ 2\).

Practical Insights

Completing the square has numerous applications in diverse disciplines like physics, engineering and economics. For instance, its application in physics helps solve projectile motion problems; by completing it you can locate the vertex of a parabola representing its trajectory which helps determine its maximum height or range.
Imagine yourself as an engineer designing a bridge. Quadratic equations allow engineers to analyze the parabolic shape of its arch using quadratic equations; by completing square, you can determine key points on this parabola and ensure your design satisfies structural requirements.

Mastering algebraic techniques like completing the square can significantly enhance your problem-solving skills in both academic and real-world scenarios. At UpStudy, we provide comprehensive resources and tools designed to help you grasp these essential mathematical concepts effortlessly.For further assistance with understanding algebraic concepts or any other mathematical challenges,explore UpStudy’s Algebra calculator!
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