Solve (7z^2 4)-(2z-6)

Question

Simplify the expression

28 z^{2} - 2 z + 6

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Factor the expression

2 (14 z^{2} - z + 3)

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Find the roots

z_{1} = \frac{1}{28} - \frac{167}{28} i, z_{2} = \frac{1}{28} + \frac{167}{28} i

Alternative Form

z_{1} \approx 0.03 \dot{5} 7142 \dot{8} - 0.46153 i, z_{2} \approx 0.03 \dot{5} 7142 \dot{8} + 0.46153 i

Evaluate

(7 z^{2} \times 4) - (2 z - 6)

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

(7 z^{2} \times 4) - (2 z - 6) = 0

Multiply the terms

28 z^{2} - (2 z - 6) = 0

If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses

28 z^{2} - 2 z + 6 = 0

Substitute a= 28,b= - 2 and c= 6 into the quadratic formula z = \frac{- b \pm b ^{2} - 4 a c}{2 a}

z = \frac{2 \pm ( - 2 ) ^{2} - 4 \times 28 \times 6}{2 \times 28}

Simplify the expression

z = \frac{2 \pm ( - 2 ) ^{2} - 4 \times 28 \times 6}{56}

Simplify the expression

More Steps

z = \frac{2 \pm - 668}{56}

Simplify the radical expression

More Steps

z = \frac{2 \pm 2 167 \times i}{56}

Separate the equation into 2 possible cases

z = \frac{2 + 2 167 \times i}{56} z = \frac{2 - 2 167 \times i}{56}

Simplify the expression

More Steps

z = \frac{1}{28} + \frac{167}{28} i z = \frac{2 - 2 167 \times i}{56}

Simplify the expression

More Steps

z = \frac{1}{28} + \frac{167}{28} i z = \frac{1}{28} - \frac{167}{28} i

Solution

z_{1} = \frac{1}{28} - \frac{167}{28} i, z_{2} = \frac{1}{28} + \frac{167}{28} i

Alternative Form

z_{1} \approx 0.03 \dot{5} 7142 \dot{8} - 0.46153 i, z_{2} \approx 0.03 \dot{5} 7142 \dot{8} + 0.46153 i

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