# What substitution should be used to rewrite 4x^{12} - 5x^{6} - 14 = 0 as a quadratic equation?

u = x^{2, }u = x^{3}, u = x^{6}, u = x^{12}

**Solution:**

The given quadratic equation is

4x^{12} - 5x^{6} - 14 = 0

Let us assume u = x^{6}

4u^{2} - 5u - 14 = 0

The standard form of the quadratic equation ax^{2} + bx + c = 0 and the formula used is

x = [-b ± √(b^{2} - 4ac)]/ 2a

Here a = 4, b = -5 and c = -14

Substituting these values in the formula

x = [-(-5) ± √((-5)^{2} - 4 × 4 × -14)]/ (2 × 4)

By further simplification

x = [5 ± √(25 + 224)]/ 8

x = [5 ± √249]/ 8

Therefore, u = x^{6} should be used to rewrite as a quadratic equation.

## What substitution should be used to rewrite 4x^{12} - 5x^{6} - 14 = 0 as a quadratic equation?

u = x^{2, }u = x^{3}, u = x^{6}, u = x^{12}

**Summary:**

The substitution u = x^{6} should be used to rewrite 4x^{12} - 5x^{6} - 14 = 0 as a quadratic equation.

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