SOLUTION: How do I solve this by using the square root property? 4x^2 - 28x + 49 = 5

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Question 417839: How do I solve this by using the square root property? 4x^2 - 28x + 49 = 5
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
4x%5E2-28x%2B49=5
Solving equations this way involves the following steps:
  1. Gather the variable terms on one side of the equation.
  2. Make a perfect square out the side of the equation with the variables.
  3. Find the square root of each side of the equation. This results in two equations! One for the positive square root and one for the negative square root.)
  4. Solve the remaining equations.
Let's see how this works:
1) Gather...
The variable terms are already just on the left side of the equation.
2) Make a perfect square...
The left side, where the variable terms are, is already a perfect square! It fits the pattern for
a%5E2-2ab%2Bb%5E2+=+%28a-b%29%5E2
with the "a" being 2x and the "b" being 7. So we can rewrite the left side as a perfect square:
%282x-7%29%5E2+=+5
3) Find the square root of each side.
sqrt%28%282x-7%29%5E2%29+=+sqrt%285%29
which simplifies to:
abs%282x-7%29+=+sqrt%285%29
which becomes:
2x-7+=+sqrt%285%29 or 2x-7+=+-sqrt%285%29
4) Solve the equations.
Adding 7 to each side:
2x+=+7+%2B+sqrt%285%29 or 2x+=+7+-+sqrt%285%29
Dividing by 2:
x+=+%287+%2B+sqrt%285%29%29%2F2 or x+=+%287+-+sqrt%285%29%29%2F2