Solve z^28z^2-6z^2 -10z^2 -7z^2-5z^2 - ScanMath

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Type your math problem... z^28z^2-6z^2 -10z^2 -7z^2-5z^2

Question

Simplify the expression

8 z^{4} - 28 z^{2}

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Factor the expression

4 z^{2} (2 z^{2} - 7)

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Find the roots

z_{1} = - \frac{14}{2}, z_{2} = 0, z_{3} = \frac{14}{2}

Alternative Form

z_{1} \approx - 1.870829, z_{2} = 0, z_{3} \approx 1.870829

Evaluate

z^{2} \times 8 z^{2} - 6 z^{2} - 10 z^{2} - 7 z^{2} - 5 z^{2}

To find the roots of the expression,set the expression equal to 0

z^{2} \times 8 z^{2} - 6 z^{2} - 10 z^{2} - 7 z^{2} - 5 z^{2} = 0

Multiply

More Steps

8 z^{4} - 6 z^{2} - 10 z^{2} - 7 z^{2} - 5 z^{2} = 0

Subtract the terms

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8 z^{4} - 16 z^{2} - 7 z^{2} - 5 z^{2} = 0

Subtract the terms

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8 z^{4} - 23 z^{2} - 5 z^{2} = 0

Subtract the terms

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8 z^{4} - 28 z^{2} = 0

Factor the expression

4 z^{2} (2 z^{2} - 7) = 0

Divide both sides

z^{2} (2 z^{2} - 7) = 0

Separate the equation into 2 possible cases

z^{2} = 0 2 z^{2} - 7 = 0

The only way a power can be 0 is when the base equals 0

z = 0 2 z^{2} - 7 = 0

Solve the equation

More Steps

z = 0 z = \frac{14}{2} z = - \frac{14}{2}

Solution

z_{1} = - \frac{14}{2}, z_{2} = 0, z_{3} = \frac{14}{2}

Alternative Form

z_{1} \approx - 1.870829, z_{2} = 0, z_{3} \approx 1.870829

Show Solution