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Simplifying -3x2 + -18x + 348 = 0 Reorder the terms: 348 + -18x + -3x2 = 0 Solving 348 + -18x + -3x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(116 + -6x + -1x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(116 + -6x + -1x2)' equal to zero and attempt to solve: Simplifying 116 + -6x + -1x2 = 0 Solving 116 + -6x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -116 + 6x + x2 = 0 Move the constant term to the right: Add '116' to each side of the equation. -116 + 6x + 116 + x2 = 0 + 116 Reorder the terms: -116 + 116 + 6x + x2 = 0 + 116 Combine like terms: -116 + 116 = 0 0 + 6x + x2 = 0 + 116 6x + x2 = 0 + 116 Combine like terms: 0 + 116 = 116 6x + x2 = 116 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 = 116 + 9 Reorder the terms: 9 + 6x + x2 = 116 + 9 Combine like terms: 116 + 9 = 125 9 + 6x + x2 = 125 Factor a perfect square on the left side: (x + 3)(x + 3) = 125 Calculate the square root of the right side: 11.180339887 Break this problem into two subproblems by setting (x + 3) equal to 11.180339887 and -11.180339887.Subproblem 1
x + 3 = 11.180339887 Simplifying x + 3 = 11.180339887 Reorder the terms: 3 + x = 11.180339887 Solving 3 + x = 11.180339887 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 = 11.180339887 + -3 Combine like terms: 3 + -3 = 0 0 + x = 11.180339887 + -3 x = 11.180339887 + -3 Combine like terms: 11.180339887 + -3 = 8.180339887 x = 8.180339887 Simplifying x = 8.180339887Subproblem 2
x + 3 = -11.180339887 Simplifying x + 3 = -11.180339887 Reorder the terms: 3 + x = -11.180339887 Solving 3 + x = -11.180339887 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 = -11.180339887 + -3 Combine like terms: 3 + -3 = 0 0 + x = -11.180339887 + -3 x = -11.180339887 + -3 Combine like terms: -11.180339887 + -3 = -14.180339887 x = -14.180339887 Simplifying x = -14.180339887Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.180339887, -14.180339887}Solution
x = {8.180339887, -14.180339887}
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