Write the quadratic equation in standard form: x^(2)+1=8x Answer:

Identify Standard Form: To write the equation in standard form, we need to have all terms on one side of the equation, resulting in a format of ax^2 + bx + c = 0.Subtract 8x: Subtract 8x from both sides of the equation x^(2) + 1 = 8x to move all terms to one side. Calculation: x^(2) + 1 - 8x = 8x - 8xAdjust Equation: After performing the subtraction, the equation becomes x^(2) - 8x + 1 = 0.Verify Standard Form: Check to ensure that all terms are correctly placed and that the equation is in standard form. The standard form of a quadratic equation is ax^2 + bx + c = 0, where a, b, and c are constants. In our case, a = 1, b = -8, and c = 1, which matches the standard form.Final Standard Form: The quadratic equation in standard form is x^(2) - 8x + 1 = 0.

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Quadratic equation with complex roots

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Q. Write the quadratic equation in standard form:

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x^{2}+1=8 x

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Answer:

Identify Standard Form: To write the equation in standard form, we need to have all terms on one side of the equation, resulting in a format of $ax^2 + bx + c = 0$ .
Subtract $8x$ : Subtract $8x$ from both sides of the equation $x^{2} + 1 = 8x$ to move all terms to one side. $\newline$ Calculation: $x^{2} + 1 - 8x = 8x - 8x$
Adjust Equation: After performing the subtraction, the equation becomes $x^{2} - 8x + 1 = 0$ .
Verify Standard Form: Check to ensure that all terms are correctly placed and that the equation is in standard form. $\newline$ The standard form of a quadratic equation is $ax^2 + bx + c = 0$ , where $a$ , $b$ , and $c$ are constants. $\newline$ In our case, $a = 1$ , $b = -8$ , and $c = 1$ , which matches the standard form.
Final Standard Form: The quadratic equation in standard form is $x^{2} - 8x + 1 = 0$ .