2x^2+12x+18=90

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Solution for 2x^2+12x+18=90 equation:


Simplifying
2x2 + 12x + 18 = 90

Reorder the terms:
18 + 12x + 2x2 = 90

Solving
18 + 12x + 2x2 = 90

Solving for variable 'x'.

Reorder the terms:
18 + -90 + 12x + 2x2 = 90 + -90

Combine like terms: 18 + -90 = -72
-72 + 12x + 2x2 = 90 + -90

Combine like terms: 90 + -90 = 0
-72 + 12x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-36 + 6x + x2) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(-36 + 6x + x2)' equal to zero and attempt to solve: Simplifying -36 + 6x + x2 = 0 Solving -36 + 6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '36' to each side of the equation. -36 + 6x + 36 + x2 = 0 + 36 Reorder the terms: -36 + 36 + 6x + x2 = 0 + 36 Combine like terms: -36 + 36 = 0 0 + 6x + x2 = 0 + 36 6x + x2 = 0 + 36 Combine like terms: 0 + 36 = 36 6x + x2 = 36 The x term is 6x. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x + 9 + x2 = 36 + 9 Reorder the terms: 9 + 6x + x2 = 36 + 9 Combine like terms: 36 + 9 = 45 9 + 6x + x2 = 45 Factor a perfect square on the left side: (x + 3)(x + 3) = 45 Calculate the square root of the right side: 6.708203933 Break this problem into two subproblems by setting (x + 3) equal to 6.708203933 and -6.708203933.

Subproblem 1

x + 3 = 6.708203933 Simplifying x + 3 = 6.708203933 Reorder the terms: 3 + x = 6.708203933 Solving 3 + x = 6.708203933 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 6.708203933 + -3 Combine like terms: 3 + -3 = 0 0 + x = 6.708203933 + -3 x = 6.708203933 + -3 Combine like terms: 6.708203933 + -3 = 3.708203933 x = 3.708203933 Simplifying x = 3.708203933

Subproblem 2

x + 3 = -6.708203933 Simplifying x + 3 = -6.708203933 Reorder the terms: 3 + x = -6.708203933 Solving 3 + x = -6.708203933 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -6.708203933 + -3 Combine like terms: 3 + -3 = 0 0 + x = -6.708203933 + -3 x = -6.708203933 + -3 Combine like terms: -6.708203933 + -3 = -9.708203933 x = -9.708203933 Simplifying x = -9.708203933

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.708203933, -9.708203933}

Solution

x = {3.708203933, -9.708203933}

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