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Algebra

Question 3 of 4

The Quadratic Formula

Question

Find the solution of \(5m^2 + 26m + 5 = 0\) using the quadratic formula

Show solution Hide solution Fully worked — 8 steps
  1. Check if it is in the form \(ax^2 + bx + c = 0\)
    \[ 5m^2 + 26m + 5 = 0 \]
  2. Identify the values of \(a\), \(b\) and \(c\)
    \[ a = 5 \qquad b = 26 \qquad c = 5 \]
  3. Use the formula to find the solutions
    \[ m = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \]
  4. Substitute the values of \(a\), \(b\) and \(c\) and solve
    \[ m = \frac{-(26) \pm \sqrt{(26)^2 - 4(5)(5)}}{2(5)} \]
  5. Evaluate each part

    \(-(26) = -26\); \((26)^2 = 676\); \(-4(5)(5) = -100\) and \(2(5) = 10\):

    \[ = \frac{-26 \pm \sqrt{676 - 100}}{10} \]
  6. Simplify under the square root

    \(676 - 100 = 576\):

    \[ = \frac{-26 \pm \sqrt{576}}{10} \]

    \(\sqrt{576} = 24\):

    \[ = \frac{-26 \pm 24}{10} \]
  7. Find the two solutions

    Then

    \[ m = \frac{-26 + 24}{10} = -\frac{1}{5} \]

    or

    \[ m = \frac{-26 - 24}{10} = -5 \]
  8. State the solutions

    So the solutions are \(m = -\frac{1}{5}\) and \(m = -5\). That is, \(m\) is minus one fifth and \(m\) is minus five.