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Simplifying 8x2 = -16x + 31 Reorder the terms: 8x2 = 31 + -16x Solving 8x2 = 31 + -16x Solving for variable 'x'. Reorder the terms: -31 + 16x + 8x2 = 31 + -16x + -31 + 16x Reorder the terms: -31 + 16x + 8x2 = 31 + -31 + -16x + 16x Combine like terms: 31 + -31 = 0 -31 + 16x + 8x2 = 0 + -16x + 16x -31 + 16x + 8x2 = -16x + 16x Combine like terms: -16x + 16x = 0 -31 + 16x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -3.875 + 2x + x2 = 0 Move the constant term to the right: Add '3.875' to each side of the equation. -3.875 + 2x + 3.875 + x2 = 0 + 3.875 Reorder the terms: -3.875 + 3.875 + 2x + x2 = 0 + 3.875 Combine like terms: -3.875 + 3.875 = 0.000 0.000 + 2x + x2 = 0 + 3.875 2x + x2 = 0 + 3.875 Combine like terms: 0 + 3.875 = 3.875 2x + x2 = 3.875 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 = 3.875 + 1 Reorder the terms: 1 + 2x + x2 = 3.875 + 1 Combine like terms: 3.875 + 1 = 4.875 1 + 2x + x2 = 4.875 Factor a perfect square on the left side: (x + 1)(x + 1) = 4.875 Calculate the square root of the right side: 2.207940217 Break this problem into two subproblems by setting (x + 1) equal to 2.207940217 and -2.207940217.Subproblem 1
x + 1 = 2.207940217 Simplifying x + 1 = 2.207940217 Reorder the terms: 1 + x = 2.207940217 Solving 1 + x = 2.207940217 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 = 2.207940217 + -1 Combine like terms: 1 + -1 = 0 0 + x = 2.207940217 + -1 x = 2.207940217 + -1 Combine like terms: 2.207940217 + -1 = 1.207940217 x = 1.207940217 Simplifying x = 1.207940217Subproblem 2
x + 1 = -2.207940217 Simplifying x + 1 = -2.207940217 Reorder the terms: 1 + x = -2.207940217 Solving 1 + x = -2.207940217 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 = -2.207940217 + -1 Combine like terms: 1 + -1 = 0 0 + x = -2.207940217 + -1 x = -2.207940217 + -1 Combine like terms: -2.207940217 + -1 = -3.207940217 x = -3.207940217 Simplifying x = -3.207940217Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.207940217, -3.207940217}
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