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Simplifying 2x2 + -4x + -16.31 = 0 Reorder the terms: -16.31 + -4x + 2x2 = 0 Solving -16.31 + -4x + 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'. -8.155 + -2x + x2 = 0 Move the constant term to the right: Add '8.155' to each side of the equation. -8.155 + -2x + 8.155 + x2 = 0 + 8.155 Reorder the terms: -8.155 + 8.155 + -2x + x2 = 0 + 8.155 Combine like terms: -8.155 + 8.155 = 0.000 0.000 + -2x + x2 = 0 + 8.155 -2x + x2 = 0 + 8.155 Combine like terms: 0 + 8.155 = 8.155 -2x + x2 = 8.155 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 = 8.155 + 1 Reorder the terms: 1 + -2x + x2 = 8.155 + 1 Combine like terms: 8.155 + 1 = 9.155 1 + -2x + x2 = 9.155 Factor a perfect square on the left side: (x + -1)(x + -1) = 9.155 Calculate the square root of the right side: 3.025723054 Break this problem into two subproblems by setting (x + -1) equal to 3.025723054 and -3.025723054.Subproblem 1
x + -1 = 3.025723054 Simplifying x + -1 = 3.025723054 Reorder the terms: -1 + x = 3.025723054 Solving -1 + x = 3.025723054 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 = 3.025723054 + 1 Combine like terms: -1 + 1 = 0 0 + x = 3.025723054 + 1 x = 3.025723054 + 1 Combine like terms: 3.025723054 + 1 = 4.025723054 x = 4.025723054 Simplifying x = 4.025723054Subproblem 2
x + -1 = -3.025723054 Simplifying x + -1 = -3.025723054 Reorder the terms: -1 + x = -3.025723054 Solving -1 + x = -3.025723054 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 = -3.025723054 + 1 Combine like terms: -1 + 1 = 0 0 + x = -3.025723054 + 1 x = -3.025723054 + 1 Combine like terms: -3.025723054 + 1 = -2.025723054 x = -2.025723054 Simplifying x = -2.025723054Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.025723054, -2.025723054}
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