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Simplifying 3x2 + -6x + -47 = 0 Reorder the terms: -47 + -6x + 3x2 = 0 Solving -47 + -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'. -15.66666667 + -2x + x2 = 0 Move the constant term to the right: Add '15.66666667' to each side of the equation. -15.66666667 + -2x + 15.66666667 + x2 = 0 + 15.66666667 Reorder the terms: -15.66666667 + 15.66666667 + -2x + x2 = 0 + 15.66666667 Combine like terms: -15.66666667 + 15.66666667 = 0.00000000 0.00000000 + -2x + x2 = 0 + 15.66666667 -2x + x2 = 0 + 15.66666667 Combine like terms: 0 + 15.66666667 = 15.66666667 -2x + x2 = 15.66666667 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 = 15.66666667 + 1 Reorder the terms: 1 + -2x + x2 = 15.66666667 + 1 Combine like terms: 15.66666667 + 1 = 16.66666667 1 + -2x + x2 = 16.66666667 Factor a perfect square on the left side: (x + -1)(x + -1) = 16.66666667 Calculate the square root of the right side: 4.082482905 Break this problem into two subproblems by setting (x + -1) equal to 4.082482905 and -4.082482905.Subproblem 1
x + -1 = 4.082482905 Simplifying x + -1 = 4.082482905 Reorder the terms: -1 + x = 4.082482905 Solving -1 + x = 4.082482905 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 = 4.082482905 + 1 Combine like terms: -1 + 1 = 0 0 + x = 4.082482905 + 1 x = 4.082482905 + 1 Combine like terms: 4.082482905 + 1 = 5.082482905 x = 5.082482905 Simplifying x = 5.082482905Subproblem 2
x + -1 = -4.082482905 Simplifying x + -1 = -4.082482905 Reorder the terms: -1 + x = -4.082482905 Solving -1 + x = -4.082482905 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 = -4.082482905 + 1 Combine like terms: -1 + 1 = 0 0 + x = -4.082482905 + 1 x = -4.082482905 + 1 Combine like terms: -4.082482905 + 1 = -3.082482905 x = -3.082482905 Simplifying x = -3.082482905Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.082482905, -3.082482905}
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