Solve 7-6u=5u^29 - ScanMath

Question

7 - 6 u = 5 u^{2} \times 9

Solve the quadratic equation

Solve by factoring

Solve using the quadratic formula

Solve by completing the square

u_{1} = - \frac{7}{15}, u_{2} = \frac{1}{3}

Alternative Form

u_{1} = - 0.4 \dot{6}, u_{2} = 0. \dot{3}

Evaluate

7 - 6 u = 5 u^{2} \times 9

Multiply the terms

7 - 6 u = 45 u^{2}

Swap the sides

45 u^{2} = 7 - 6 u

Move the expression to the left side

45 u^{2} - 7 + 6 u = 0

Factor the expression

More Steps

Evaluate

45 u^{2} - 7 + 6 u

Reorder the terms

45 u^{2} + 6 u - 7

Rewrite the expression

45 u^{2} + (21 - 15) u - 7

Calculate

45 u^{2} + 21 u - 15 u - 7

Rewrite the expression

3 u \times 15 u + 3 u \times 7 - 15 u - 7

Factor out 3 u from the expression

3 u (15 u + 7) - 15 u - 7

Factor out - 1 from the expression

3 u (15 u + 7) - (15 u + 7)

Factor out 15 u + 7 from the expression

(3 u - 1) (15 u + 7)

(3 u - 1) (15 u + 7) = 0

When the product of factors equals 0,at least one factor is 0

3 u - 1 = 0 15 u + 7 = 0

Solve the equation for u

More Steps

Evaluate

3 u - 1 = 0

Move the constant to the right-hand side and change its sign

3 u = 0 + 1

Removing 0 doesn't change the value,so remove it from the expression

3 u = 1

Divide both sides

\frac{3 u}{3} = \frac{1}{3}

Divide the numbers

u = \frac{1}{3}

u = \frac{1}{3} 15 u + 7 = 0

Solve the equation for u

More Steps

Evaluate

15 u + 7 = 0

Move the constant to the right-hand side and change its sign

15 u = 0 - 7

Removing 0 doesn't change the value,so remove it from the expression

15 u = - 7

Divide both sides

\frac{15 u}{15} = \frac{- 7}{15}

Divide the numbers

u = \frac{- 7}{15}

Use \frac{- a}{b} = \frac{a}{- b} = - \frac{a}{b} to rewrite the fraction

u = - \frac{7}{15}

u = \frac{1}{3} u = - \frac{7}{15}

Solution

u_{1} = - \frac{7}{15}, u_{2} = \frac{1}{3}

Alternative Form

u_{1} = - 0.4 \dot{6}, u_{2} = 0. \dot{3}

Show Solution