3x^2+72x+402=0

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Solution for 3x^2+72x+402=0 equation:


Simplifying
3x2 + 72x + 402 = 0

Reorder the terms:
402 + 72x + 3x2 = 0

Solving
402 + 72x + 3x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(134 + 24x + x2) = 0

Ignore the factor 3.

Subproblem 1

Set the factor '(134 + 24x + x2)' equal to zero and attempt to solve: Simplifying 134 + 24x + x2 = 0 Solving 134 + 24x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-134' to each side of the equation. 134 + 24x + -134 + x2 = 0 + -134 Reorder the terms: 134 + -134 + 24x + x2 = 0 + -134 Combine like terms: 134 + -134 = 0 0 + 24x + x2 = 0 + -134 24x + x2 = 0 + -134 Combine like terms: 0 + -134 = -134 24x + x2 = -134 The x term is 24x. Take half its coefficient (12). Square it (144) and add it to both sides. Add '144' to each side of the equation. 24x + 144 + x2 = -134 + 144 Reorder the terms: 144 + 24x + x2 = -134 + 144 Combine like terms: -134 + 144 = 10 144 + 24x + x2 = 10 Factor a perfect square on the left side: (x + 12)(x + 12) = 10 Calculate the square root of the right side: 3.16227766 Break this problem into two subproblems by setting (x + 12) equal to 3.16227766 and -3.16227766.

Subproblem 1

x + 12 = 3.16227766 Simplifying x + 12 = 3.16227766 Reorder the terms: 12 + x = 3.16227766 Solving 12 + x = 3.16227766 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + x = 3.16227766 + -12 Combine like terms: 12 + -12 = 0 0 + x = 3.16227766 + -12 x = 3.16227766 + -12 Combine like terms: 3.16227766 + -12 = -8.83772234 x = -8.83772234 Simplifying x = -8.83772234

Subproblem 2

x + 12 = -3.16227766 Simplifying x + 12 = -3.16227766 Reorder the terms: 12 + x = -3.16227766 Solving 12 + x = -3.16227766 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + x = -3.16227766 + -12 Combine like terms: 12 + -12 = 0 0 + x = -3.16227766 + -12 x = -3.16227766 + -12 Combine like terms: -3.16227766 + -12 = -15.16227766 x = -15.16227766 Simplifying x = -15.16227766

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-8.83772234, -15.16227766}

Solution

x = {-8.83772234, -15.16227766}

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