3x2 - 4x + 1 = 0 by perfect square method
Answers
Answer:
Move the constant term to the other side of the equation. Add 5 to both sides of the equation: x² + 4x - 5= 0 => x² + 4x = 5
Divide every term by the coefficient of the x² term, in this case that coefficient is 1, so I will omit this step.
Find the square of half of the linear term’s coefficient: (4/2)² = 4
Add the result of step 2, the square of half of the linear term’s coefficient, to both sides of the equation. x² + 4x = 5 => x² + 4x + 4 = 5 + 4
Simplify the right hand side: x² + 4x + 4 = 9
Rewrite the left hand side trinomial as a perfect square binomial. It should be (x + 2)², the constant for this binomial, should be half the coefficient of the linear term of the trinomial, which should also be the square root of the constant term of the trinomial, in number case(
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) 2, because the linear term had a coefficient of 4. x² 4x + 4 = 9 => (x + 2)² = 9
Take the square root of both number, remember that the square root of an rational number includes both a positive and negative solution. √(x + 2)² = ±√9 => x + 2 = ±3
Add the opposite of the constant to both sides to isolate the variable,