x(3x+12)+90=180

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Solution for x(3x+12)+90=180 equation:


Simplifying
x(3x + 12) + 90 = 180

Reorder the terms:
x(12 + 3x) + 90 = 180
(12 * x + 3x * x) + 90 = 180
(12x + 3x2) + 90 = 180

Reorder the terms:
90 + 12x + 3x2 = 180

Solving
90 + 12x + 3x2 = 180

Solving for variable 'x'.

Reorder the terms:
90 + -180 + 12x + 3x2 = 180 + -180

Combine like terms: 90 + -180 = -90
-90 + 12x + 3x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-90 + 12x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-30 + 4x + x2) = 0

Ignore the factor 3.

Subproblem 1

Set the factor '(-30 + 4x + x2)' equal to zero and attempt to solve: Simplifying -30 + 4x + x2 = 0 Solving -30 + 4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '30' to each side of the equation. -30 + 4x + 30 + x2 = 0 + 30 Reorder the terms: -30 + 30 + 4x + x2 = 0 + 30 Combine like terms: -30 + 30 = 0 0 + 4x + x2 = 0 + 30 4x + x2 = 0 + 30 Combine like terms: 0 + 30 = 30 4x + x2 = 30 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = 30 + 4 Reorder the terms: 4 + 4x + x2 = 30 + 4 Combine like terms: 30 + 4 = 34 4 + 4x + x2 = 34 Factor a perfect square on the left side: (x + 2)(x + 2) = 34 Calculate the square root of the right side: 5.830951895 Break this problem into two subproblems by setting (x + 2) equal to 5.830951895 and -5.830951895.

Subproblem 1

x + 2 = 5.830951895 Simplifying x + 2 = 5.830951895 Reorder the terms: 2 + x = 5.830951895 Solving 2 + x = 5.830951895 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 5.830951895 + -2 Combine like terms: 2 + -2 = 0 0 + x = 5.830951895 + -2 x = 5.830951895 + -2 Combine like terms: 5.830951895 + -2 = 3.830951895 x = 3.830951895 Simplifying x = 3.830951895

Subproblem 2

x + 2 = -5.830951895 Simplifying x + 2 = -5.830951895 Reorder the terms: 2 + x = -5.830951895 Solving 2 + x = -5.830951895 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -5.830951895 + -2 Combine like terms: 2 + -2 = 0 0 + x = -5.830951895 + -2 x = -5.830951895 + -2 Combine like terms: -5.830951895 + -2 = -7.830951895 x = -7.830951895 Simplifying x = -7.830951895

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.830951895, -7.830951895}

Solution

x = {3.830951895, -7.830951895}

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