Question
Write the quadratic equation in standard form:
x, squared, minus, 5, x, plus, 13, equals, 1
x
2
−5x+13=
1
x, squared, minus, 5, x, plus, 13, equals, 1
x
2
−5x+13=
1
Answers
Answered by
GPT-4o mini
To write the quadratic equation in standard form, we need to move all the terms to one side of the equation. Starting with:
\[ x^2 - 5x + 13 = 1 \]
we can subtract 1 from both sides:
\[ x^2 - 5x + 13 - 1 = 0 \]
This simplifies to:
\[ x^2 - 5x + 12 = 0 \]
Now the equation is in standard form \( ax^2 + bx + c = 0 \), where \( a = 1 \), \( b = -5 \), and \( c = 12 \). So the final standard form of the quadratic equation is:
\[ x^2 - 5x + 12 = 0 \]
\[ x^2 - 5x + 13 = 1 \]
we can subtract 1 from both sides:
\[ x^2 - 5x + 13 - 1 = 0 \]
This simplifies to:
\[ x^2 - 5x + 12 = 0 \]
Now the equation is in standard form \( ax^2 + bx + c = 0 \), where \( a = 1 \), \( b = -5 \), and \( c = 12 \). So the final standard form of the quadratic equation is:
\[ x^2 - 5x + 12 = 0 \]