π(r+6) ² = 15(2πr) + 2 πr²?

Math lovers of the world! -Please complete this equation for me, step by step.. Much thanks :)

π(r+6) ² = 15(2πr) + 2 πr²

~Michelle

5 Answers

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  • KY
    Lv 7
    1 decade ago
    Favorite Answer

    π(r+6) ² = 15(2πr) + 2 πr²

    First, recognize that since everything on both sides of the equal is being multiplied by π, it can be factored out of the equation entirely.

    π(r+6) ² = 15(2πr) + 2 πr²

    π(r+6) ² = π[15(2r) + 2r²]

    (r+6) ² = [15(2r) + 2r²]

    >> multiply out the parenthetical expressions

    (r² + 12r + 36) = 30r + 2r²

    r² + 12r + 36 = 30r + 2r²

    >> move everything to one side of the equal sign

    0 = r² + 18r - 36

    >> solve for r using the quadratic formula

    r = (1/2)[-18 ± √(324+144)]

    >> simplify using rules of algebra for radicals

    r = (1/2)(-18) ± (1/2)√(468)

    r = -9 ± (1/2)√468

    r = -9 ± (1/2)√(36*13)

    r = -9 ± (1/2)(6)√13

    r = -9 ± 3√13

    ANSWER

    r = -9 + 3√13

    r = -9 - 3√13

  • 1 decade ago

    The π is just a distraction.

  • 1 decade ago

    Those answers check out ok in Microsoft Excel

  • 1 decade ago

    It looks like it's going to be a weird quadratic equation.

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  • 1 decade ago

    ugh.

    Lose the π and work from there.

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