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Simplifying 2x2 + -8x + -111 = 0 Reorder the terms: -111 + -8x + 2x2 = 0 Solving -111 + -8x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -55.5 + -4x + x2 = 0 Move the constant term to the right: Add '55.5' to each side of the equation. -55.5 + -4x + 55.5 + x2 = 0 + 55.5 Reorder the terms: -55.5 + 55.5 + -4x + x2 = 0 + 55.5 Combine like terms: -55.5 + 55.5 = 0.0 0.0 + -4x + x2 = 0 + 55.5 -4x + x2 = 0 + 55.5 Combine like terms: 0 + 55.5 = 55.5 -4x + x2 = 55.5 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = 55.5 + 4 Reorder the terms: 4 + -4x + x2 = 55.5 + 4 Combine like terms: 55.5 + 4 = 59.5 4 + -4x + x2 = 59.5 Factor a perfect square on the left side: (x + -2)(x + -2) = 59.5 Calculate the square root of the right side: 7.71362431 Break this problem into two subproblems by setting (x + -2) equal to 7.71362431 and -7.71362431.Subproblem 1
x + -2 = 7.71362431 Simplifying x + -2 = 7.71362431 Reorder the terms: -2 + x = 7.71362431 Solving -2 + x = 7.71362431 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 7.71362431 + 2 Combine like terms: -2 + 2 = 0 0 + x = 7.71362431 + 2 x = 7.71362431 + 2 Combine like terms: 7.71362431 + 2 = 9.71362431 x = 9.71362431 Simplifying x = 9.71362431Subproblem 2
x + -2 = -7.71362431 Simplifying x + -2 = -7.71362431 Reorder the terms: -2 + x = -7.71362431 Solving -2 + x = -7.71362431 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -7.71362431 + 2 Combine like terms: -2 + 2 = 0 0 + x = -7.71362431 + 2 x = -7.71362431 + 2 Combine like terms: -7.71362431 + 2 = -5.71362431 x = -5.71362431 Simplifying x = -5.71362431Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.71362431, -5.71362431}
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