Find the roots of the following quadratic equation by splitting the middle term x2+20x+99=0​

Question

Find the roots of the following quadratic equation by splitting the
middle term x2+20x+99=0​

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Gabriella 4 weeks 2021-08-15T06:22:11+00:00 1 Answer 0 views 0

Answers ( )

    0
    2021-08-15T06:23:36+00:00

    Answer:

    x^2 +20+99 = 0

    Simplifying

    x2 + -20x + 99 = 0

    Reorder the terms:

    99 + -20x + x2 = 0

    Solving

    99 + -20x + x2 = 0

    Solving for variable ‘x’.

    Factor a trinomial.

    (9 + -1x)(11 + -1x) = 0

    Subproblem 1

    Set the factor ‘(9 + -1x)’ equal to zero and attempt to solve:

    Simplifying

    9 + -1x = 0

    Solving

    9 + -1x = 0

    Move all terms containing x to the left, all other terms to the right.

    Add ‘-9’ to each side of the equation.

    9 + -9 + -1x = 0 + -9

    Combine like terms: 9 + -9 = 0

    0 + -1x = 0 + -9

    -1x = 0 + -9

    Combine like terms: 0 + -9 = -9

    -1x = -9

    Divide each side by ‘-1’.

    x = 9

    Simplifying

    x = 9

    Subproblem 2

    Set the factor ‘(11 + -1x)’ equal to zero and attempt to solve:

    Simplifying

    11 + -1x = 0

    Solving

    11 + -1x = 0

    Move all terms containing x to the left, all other terms to the right.

    Add ‘-11’ to each side of the equation.

    11 + -11 + -1x = 0 + -11

    Combine like terms: 11 + -11 = 0

    0 + -1x = 0 + -11

    -1x = 0 + -11

    Combine like terms: 0 + -11 = -11

    -1x = -11

    Divide each side by ‘-1’.

    x = 11

    Simplifying

    x = 11

    Solution

    x = {9, 11}

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