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Simplifying 3x2 + -6x + -92 = 0 Reorder the terms: -92 + -6x + 3x2 = 0 Solving -92 + -6x + 3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -30.66666667 + -2x + x2 = 0 Move the constant term to the right: Add '30.66666667' to each side of the equation. -30.66666667 + -2x + 30.66666667 + x2 = 0 + 30.66666667 Reorder the terms: -30.66666667 + 30.66666667 + -2x + x2 = 0 + 30.66666667 Combine like terms: -30.66666667 + 30.66666667 = 0.00000000 0.00000000 + -2x + x2 = 0 + 30.66666667 -2x + x2 = 0 + 30.66666667 Combine like terms: 0 + 30.66666667 = 30.66666667 -2x + x2 = 30.66666667 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 30.66666667 + 1 Reorder the terms: 1 + -2x + x2 = 30.66666667 + 1 Combine like terms: 30.66666667 + 1 = 31.66666667 1 + -2x + x2 = 31.66666667 Factor a perfect square on the left side: (x + -1)(x + -1) = 31.66666667 Calculate the square root of the right side: 5.627314339 Break this problem into two subproblems by setting (x + -1) equal to 5.627314339 and -5.627314339.Subproblem 1
x + -1 = 5.627314339 Simplifying x + -1 = 5.627314339 Reorder the terms: -1 + x = 5.627314339 Solving -1 + x = 5.627314339 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 5.627314339 + 1 Combine like terms: -1 + 1 = 0 0 + x = 5.627314339 + 1 x = 5.627314339 + 1 Combine like terms: 5.627314339 + 1 = 6.627314339 x = 6.627314339 Simplifying x = 6.627314339Subproblem 2
x + -1 = -5.627314339 Simplifying x + -1 = -5.627314339 Reorder the terms: -1 + x = -5.627314339 Solving -1 + x = -5.627314339 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -5.627314339 + 1 Combine like terms: -1 + 1 = 0 0 + x = -5.627314339 + 1 x = -5.627314339 + 1 Combine like terms: -5.627314339 + 1 = -4.627314339 x = -4.627314339 Simplifying x = -4.627314339Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.627314339, -4.627314339}
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