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Simplifying 0 = 2x2 + 12x + -378 Reorder the terms: 0 = -378 + 12x + 2x2 Solving 0 = -378 + 12x + 2x2 Solving for variable 'x'. Combine like terms: 0 + 378 = 378 378 + -12x + -2x2 = -378 + 12x + 2x2 + 378 + -12x + -2x2 Reorder the terms: 378 + -12x + -2x2 = -378 + 378 + 12x + -12x + 2x2 + -2x2 Combine like terms: -378 + 378 = 0 378 + -12x + -2x2 = 0 + 12x + -12x + 2x2 + -2x2 378 + -12x + -2x2 = 12x + -12x + 2x2 + -2x2 Combine like terms: 12x + -12x = 0 378 + -12x + -2x2 = 0 + 2x2 + -2x2 378 + -12x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 378 + -12x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(189 + -6x + -1x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(189 + -6x + -1x2)' equal to zero and attempt to solve: Simplifying 189 + -6x + -1x2 = 0 Solving 189 + -6x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -189 + 6x + x2 = 0 Move the constant term to the right: Add '189' to each side of the equation. -189 + 6x + 189 + x2 = 0 + 189 Reorder the terms: -189 + 189 + 6x + x2 = 0 + 189 Combine like terms: -189 + 189 = 0 0 + 6x + x2 = 0 + 189 6x + x2 = 0 + 189 Combine like terms: 0 + 189 = 189 6x + x2 = 189 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 = 189 + 9 Reorder the terms: 9 + 6x + x2 = 189 + 9 Combine like terms: 189 + 9 = 198 9 + 6x + x2 = 198 Factor a perfect square on the left side: (x + 3)(x + 3) = 198 Calculate the square root of the right side: 14.071247279 Break this problem into two subproblems by setting (x + 3) equal to 14.071247279 and -14.071247279.Subproblem 1
x + 3 = 14.071247279 Simplifying x + 3 = 14.071247279 Reorder the terms: 3 + x = 14.071247279 Solving 3 + x = 14.071247279 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 = 14.071247279 + -3 Combine like terms: 3 + -3 = 0 0 + x = 14.071247279 + -3 x = 14.071247279 + -3 Combine like terms: 14.071247279 + -3 = 11.071247279 x = 11.071247279 Simplifying x = 11.071247279Subproblem 2
x + 3 = -14.071247279 Simplifying x + 3 = -14.071247279 Reorder the terms: 3 + x = -14.071247279 Solving 3 + x = -14.071247279 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 = -14.071247279 + -3 Combine like terms: 3 + -3 = 0 0 + x = -14.071247279 + -3 x = -14.071247279 + -3 Combine like terms: -14.071247279 + -3 = -17.071247279 x = -17.071247279 Simplifying x = -17.071247279Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.071247279, -17.071247279}Solution
x = {11.071247279, -17.071247279}
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