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Simplifying -78 + -7x + 2x2 = 0 Solving -78 + -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'. -39 + -3.5x + x2 = 0 Move the constant term to the right: Add '39' to each side of the equation. -39 + -3.5x + 39 + x2 = 0 + 39 Reorder the terms: -39 + 39 + -3.5x + x2 = 0 + 39 Combine like terms: -39 + 39 = 0 0 + -3.5x + x2 = 0 + 39 -3.5x + x2 = 0 + 39 Combine like terms: 0 + 39 = 39 -3.5x + x2 = 39 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 = 39 + 3.0625 Reorder the terms: 3.0625 + -3.5x + x2 = 39 + 3.0625 Combine like terms: 39 + 3.0625 = 42.0625 3.0625 + -3.5x + x2 = 42.0625 Factor a perfect square on the left side: (x + -1.75)(x + -1.75) = 42.0625 Calculate the square root of the right side: 6.485560886 Break this problem into two subproblems by setting (x + -1.75) equal to 6.485560886 and -6.485560886.Subproblem 1
x + -1.75 = 6.485560886 Simplifying x + -1.75 = 6.485560886 Reorder the terms: -1.75 + x = 6.485560886 Solving -1.75 + x = 6.485560886 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 = 6.485560886 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + x = 6.485560886 + 1.75 x = 6.485560886 + 1.75 Combine like terms: 6.485560886 + 1.75 = 8.235560886 x = 8.235560886 Simplifying x = 8.235560886Subproblem 2
x + -1.75 = -6.485560886 Simplifying x + -1.75 = -6.485560886 Reorder the terms: -1.75 + x = -6.485560886 Solving -1.75 + x = -6.485560886 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 = -6.485560886 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + x = -6.485560886 + 1.75 x = -6.485560886 + 1.75 Combine like terms: -6.485560886 + 1.75 = -4.735560886 x = -4.735560886 Simplifying x = -4.735560886Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.235560886, -4.735560886}
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