Question

36x²+23=60x
Chapter - quadratic equations

Answer 1

Answer:

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Answer 2

Solution!!

→ 36x² + 23 = 60x

Move the variable to the left-hand side and change its sign.

→ 36x² + 23 - 60x = 0

Use the commutative property to reorder the terms.

→ 36x² - 60x + 23 = 0

Comparing it with ax² + bx + c = 0; a = 36, b = -60, c = 23. Use the quadratic formula $\sf x=\dfrac{-b\pm \sqrt{b^{2}-4ac}}{2a}$ to find the value of x.

→ $\sf x=\dfrac{-b\pm \sqrt{b^{2}-4ac}}{2a}$

Substituting the values.

→ $\sf x=\dfrac{-(-60)\pm \sqrt{(-60)^{2}-4\times 36\times 23}}{2(36)}$

When there is a minus in front of an expression in parentheses, change the sign of each term in the expression.

→ $\sf x=\dfrac{60\pm \sqrt{(-60)^{2}-4\times 36\times 23}}{2(36)}$

Evaluate the power.

→ $\sf x=\dfrac{60\pm \sqrt{3600-4\times 36\times 23}}{2(36)}$

Calculate the product.

→ $\sf x=\dfrac{60\pm \sqrt{3600-3312}}{2(36)}$

Multiply the numbers.

→ $\sf x=\dfrac{60\pm \sqrt{3600-3312}}{72}$

Subtract the numbers.

→ $\sf x=\dfrac{60\pm \sqrt{288}}{72}$

Simplify the radical expression.

→ $\sf x=\dfrac{60\pm 12\sqrt{2}}{72}$

Write the solutions, one with a + sign and one with a - sign.

→ $\sf x=\dfrac{60+12\sqrt{2}}{72}$

→ $\sf x=\dfrac{60-12\sqrt{2}}{72}$

Factor out 12 from the expressions.

→ $\sf x=\dfrac{12(5+\sqrt{2})}{72}$

→ $\sf x=\dfrac{12(5-\sqrt{2})}{72}$

Simplify the expressions.

→ $\sf x=\dfrac{5+\sqrt{2}}{6}$

→ $\sf x=\dfrac{5-\sqrt{2}}{6}$

Hence, we have two values for x.