Solve 7x(-7x 1)-23-2(-7x 1)13

Question

Simplify the expression

- 49 x^{2} - 23 + 182 x

Show Solution

x_{1} = \frac{13 - 146}{7}, x_{2} = \frac{13 + 146}{7}

Alternative Form

x_{1} \approx 0.130993, x_{2} \approx 3.583292

Evaluate

7 x (- 7 x \times 1) - 23 - 2 (- 7 x \times 1) \times 13

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

7 x (- 7 x \times 1) - 23 - 2 (- 7 x \times 1) \times 13 = 0

Multiply the terms

7 x (- 7 x) - 23 - 2 (- 7 x \times 1) \times 13 = 0

Multiply the terms

7 x (- 7 x) - 23 - 2 (- 7 x) \times 13 = 0

Multiply

More Steps

- 49 x^{2} - 23 - 2 (- 7 x) \times 13 = 0

Multiply

More Steps

- 49 x^{2} - 23 - (- 182 x) = 0

Rewrite the expression

- 49 x^{2} - 23 + 182 x = 0

Rewrite in standard form

- 49 x^{2} + 182 x - 23 = 0

Multiply both sides

49 x^{2} - 182 x + 23 = 0

Substitute a= 49,b= - 182 and c= 23 into the quadratic formula x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

x = \frac{182 \pm ( - 182 ) ^{2} - 4 \times 49 \times 23}{2 \times 49}

Simplify the expression

x = \frac{182 \pm ( - 182 ) ^{2} - 4 \times 49 \times 23}{98}

Simplify the expression

More Steps

x = \frac{182 \pm 28616}{98}

Simplify the radical expression

More Steps

x = \frac{182 \pm 14 146}{98}

Separate the equation into 2 possible cases

x = \frac{182 + 14 146}{98} x = \frac{182 - 14 146}{98}

Simplify the expression

More Steps

x = \frac{13 + 146}{7} x = \frac{182 - 14 146}{98}

Simplify the expression

More Steps

x = \frac{13 + 146}{7} x = \frac{13 - 146}{7}

Solution

x_{1} = \frac{13 - 146}{7}, x_{2} = \frac{13 + 146}{7}

Alternative Form

x_{1} \approx 0.130993, x_{2} \approx 3.583292

Show Solution