Math, asked by sudender9315, 7 months ago

find the value of X X2+3X-30=0​

Answers

Answered by PSanthosh
0

Answer:

Step-by-step explanation:

  • First simplifying,

x^2 + 3x - 30 = 0

  • Next reorder the terms,

-30 + 3x + x^2 = 0

  • Solving for variable 'x'

-30 + 3x + x^2 = 0

  • Begin completing the square.

Move the constant term to the right:

  • Add '30' to each side of the equation.

-30 + 3x + 30 + x^2 = 0 + 30

  • Reorder the terms:

-30 + 30 + 3x + x^2 = 0 + 30

  • Combine like terms: -30 + 30 = 0

0 + 3x + x^2 = 0 + 30

3x + x^2 = 0 + 30

  • Combine like terms: 0 + 30 = 30

3x + x^2 = 30

  • The x term is 3x.  Take half its coefficient (1.5).

Square it (2.25) and add it to both sides.

  • Add '2.25' to each side of the equation.

3x + 2.25 + x^2 = 30 + 2.25

  • Reorder the terms:

2.25 + 3x + x^2 = 30 + 2.25

  • Combine like terms: 30 + 2.25 = 32.25

2.25 + 3x + x^2 = 32.25

  • Factor a perfect square on the left side:

(x + 1.5)(x + 1.5) = 32.25

  • Calculate the square root of the right side: 5.678908346

  • Break this problem into two subproblems by setting

(x + 1.5) equal to 5.678908346 and -5.678908346.

Case 1

x + 1.5 = 5.678908346

  • Simplifying

x + 1.5 = 5.678908346

  • Reorder the terms:

1.5 + x = 5.678908346

  • Solving for variable 'x'.

1.5 + x = 5.678908346

  • Move all terms containing x to the left, all other terms to the right.

  • Add '-1.5' to each side of the equation.

1.5 + -1.5 + x = 5.678908346 + -1.5

  • Combine like terms: 1.5 + -1.5 = 0.0

0.0 + x = 5.678908346 + -1.5

x = 5.678908346 + -1.5

  • Combine like terms: 5.678908346 + -1.5 = 4.178908346

x = 4.178908346

  • Simplifying

x = 4.178908346

Case 2

x + 1.5 = -5.678908346

  • Simplifying

x + 1.5 = -5.678908346

  • Reorder the terms:

1.5 + x = -5.678908346

  • Solving for variable 'x'.

1.5 + x = -5.678908346

  • Move all terms containing x to the left, all other terms to the right.

  • Add '-1.5' to each side of the equation.

1.5 + -1.5 + x = -5.678908346 + -1.5

  • Combine like terms: 1.5 + -1.5 = 0.0

0.0 + x = -5.678908346 + -1.5

x = -5.678908346 + -1.5

  • Combine like terms: -5.678908346 + -1.5 = -7.178908346

x = -7.178908346

  • Simplifying

x = -7.178908346

Solution

The solution to the problem is based on the solutions

from the two cases,

x = {4.178908346, -7.178908346}

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