3x^2+48x=-186

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Solution for 3x^2+48x=-186 equation:


Simplifying
3x2 + 48x = -186

Reorder the terms:
48x + 3x2 = -186

Solving
48x + 3x2 = -186

Solving for variable 'x'.

Reorder the terms:
186 + 48x + 3x2 = -186 + 186

Combine like terms: -186 + 186 = 0
186 + 48x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(62 + 16x + x2) = 0

Ignore the factor 3.

Subproblem 1

Set the factor '(62 + 16x + x2)' equal to zero and attempt to solve: Simplifying 62 + 16x + x2 = 0 Solving 62 + 16x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-62' to each side of the equation. 62 + 16x + -62 + x2 = 0 + -62 Reorder the terms: 62 + -62 + 16x + x2 = 0 + -62 Combine like terms: 62 + -62 = 0 0 + 16x + x2 = 0 + -62 16x + x2 = 0 + -62 Combine like terms: 0 + -62 = -62 16x + x2 = -62 The x term is 16x. Take half its coefficient (8). Square it (64) and add it to both sides. Add '64' to each side of the equation. 16x + 64 + x2 = -62 + 64 Reorder the terms: 64 + 16x + x2 = -62 + 64 Combine like terms: -62 + 64 = 2 64 + 16x + x2 = 2 Factor a perfect square on the left side: (x + 8)(x + 8) = 2 Calculate the square root of the right side: 1.414213562 Break this problem into two subproblems by setting (x + 8) equal to 1.414213562 and -1.414213562.

Subproblem 1

x + 8 = 1.414213562 Simplifying x + 8 = 1.414213562 Reorder the terms: 8 + x = 1.414213562 Solving 8 + x = 1.414213562 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + x = 1.414213562 + -8 Combine like terms: 8 + -8 = 0 0 + x = 1.414213562 + -8 x = 1.414213562 + -8 Combine like terms: 1.414213562 + -8 = -6.585786438 x = -6.585786438 Simplifying x = -6.585786438

Subproblem 2

x + 8 = -1.414213562 Simplifying x + 8 = -1.414213562 Reorder the terms: 8 + x = -1.414213562 Solving 8 + x = -1.414213562 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + x = -1.414213562 + -8 Combine like terms: 8 + -8 = 0 0 + x = -1.414213562 + -8 x = -1.414213562 + -8 Combine like terms: -1.414213562 + -8 = -9.414213562 x = -9.414213562 Simplifying x = -9.414213562

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-6.585786438, -9.414213562}

Solution

x = {-6.585786438, -9.414213562}

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