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Simplifying 2x2 + -7x + -8 = 0 Reorder the terms: -8 + -7x + 2x2 = 0 Solving -8 + -7x + 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'. -4 + -3.5x + x2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + -3.5x + 4 + x2 = 0 + 4 Reorder the terms: -4 + 4 + -3.5x + x2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -3.5x + x2 = 0 + 4 -3.5x + x2 = 0 + 4 Combine like terms: 0 + 4 = 4 -3.5x + x2 = 4 The x term is -3.5x. Take half its coefficient (-1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. -3.5x + 3.0625 + x2 = 4 + 3.0625 Reorder the terms: 3.0625 + -3.5x + x2 = 4 + 3.0625 Combine like terms: 4 + 3.0625 = 7.0625 3.0625 + -3.5x + x2 = 7.0625 Factor a perfect square on the left side: (x + -1.75)(x + -1.75) = 7.0625 Calculate the square root of the right side: 2.657536453 Break this problem into two subproblems by setting (x + -1.75) equal to 2.657536453 and -2.657536453.Subproblem 1
x + -1.75 = 2.657536453 Simplifying x + -1.75 = 2.657536453 Reorder the terms: -1.75 + x = 2.657536453 Solving -1.75 + x = 2.657536453 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + x = 2.657536453 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + x = 2.657536453 + 1.75 x = 2.657536453 + 1.75 Combine like terms: 2.657536453 + 1.75 = 4.407536453 x = 4.407536453 Simplifying x = 4.407536453Subproblem 2
x + -1.75 = -2.657536453 Simplifying x + -1.75 = -2.657536453 Reorder the terms: -1.75 + x = -2.657536453 Solving -1.75 + x = -2.657536453 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + x = -2.657536453 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + x = -2.657536453 + 1.75 x = -2.657536453 + 1.75 Combine like terms: -2.657536453 + 1.75 = -0.907536453 x = -0.907536453 Simplifying x = -0.907536453Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.407536453, -0.907536453}
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