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Simplifying -3x2 + -6x + 56 = 0 Reorder the terms: 56 + -6x + -3x2 = 0 Solving 56 + -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'. -18.66666667 + 2x + x2 = 0 Move the constant term to the right: Add '18.66666667' to each side of the equation. -18.66666667 + 2x + 18.66666667 + x2 = 0 + 18.66666667 Reorder the terms: -18.66666667 + 18.66666667 + 2x + x2 = 0 + 18.66666667 Combine like terms: -18.66666667 + 18.66666667 = 0.00000000 0.00000000 + 2x + x2 = 0 + 18.66666667 2x + x2 = 0 + 18.66666667 Combine like terms: 0 + 18.66666667 = 18.66666667 2x + x2 = 18.66666667 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 = 18.66666667 + 1 Reorder the terms: 1 + 2x + x2 = 18.66666667 + 1 Combine like terms: 18.66666667 + 1 = 19.66666667 1 + 2x + x2 = 19.66666667 Factor a perfect square on the left side: (x + 1)(x + 1) = 19.66666667 Calculate the square root of the right side: 4.434711566 Break this problem into two subproblems by setting (x + 1) equal to 4.434711566 and -4.434711566.Subproblem 1
x + 1 = 4.434711566 Simplifying x + 1 = 4.434711566 Reorder the terms: 1 + x = 4.434711566 Solving 1 + x = 4.434711566 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 = 4.434711566 + -1 Combine like terms: 1 + -1 = 0 0 + x = 4.434711566 + -1 x = 4.434711566 + -1 Combine like terms: 4.434711566 + -1 = 3.434711566 x = 3.434711566 Simplifying x = 3.434711566Subproblem 2
x + 1 = -4.434711566 Simplifying x + 1 = -4.434711566 Reorder the terms: 1 + x = -4.434711566 Solving 1 + x = -4.434711566 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 = -4.434711566 + -1 Combine like terms: 1 + -1 = 0 0 + x = -4.434711566 + -1 x = -4.434711566 + -1 Combine like terms: -4.434711566 + -1 = -5.434711566 x = -5.434711566 Simplifying x = -5.434711566Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.434711566, -5.434711566}
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