Solve 109f -4f 10f-1-f - Socratic AI (ScanMath)

Question

Simplify the expression

108 f - 40 f^{2} - 1

Show Solution

f_{1} = \frac{27 - 719}{20}, f_{2} = \frac{27 + 719}{20}

Alternative Form

f_{1} \approx 0.009291, f_{2} \approx 2.690709

Evaluate

109 f - 4 f \times 10 f - 1 - f

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

109 f - 4 f \times 10 f - 1 - f = 0

Multiply

More Steps

109 f - 40 f^{2} - 1 - f = 0

Subtract the terms

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108 f - 40 f^{2} - 1 = 0

Rewrite in standard form

- 40 f^{2} + 108 f - 1 = 0

Multiply both sides

40 f^{2} - 108 f + 1 = 0

Substitute a= 40,b= - 108 and c= 1 into the quadratic formula f = \frac{- b \pm b ^{2} - 4 a c}{2 a}

f = \frac{108 \pm ( - 108 ) ^{2} - 4 \times 40}{2 \times 40}

Simplify the expression

f = \frac{108 \pm ( - 108 ) ^{2} - 4 \times 40}{80}

Simplify the expression

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f = \frac{108 \pm 11504}{80}

Simplify the radical expression

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f = \frac{108 \pm 4 719}{80}

Separate the equation into 2 possible cases

f = \frac{108 + 4 719}{80} f = \frac{108 - 4 719}{80}

Simplify the expression

More Steps

f = \frac{27 + 719}{20} f = \frac{108 - 4 719}{80}

Simplify the expression

More Steps

f = \frac{27 + 719}{20} f = \frac{27 - 719}{20}

Solution

f_{1} = \frac{27 - 719}{20}, f_{2} = \frac{27 + 719}{20}

Alternative Form

f_{1} \approx 0.009291, f_{2} \approx 2.690709

Show Solution