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Simplifying 2x2 + -2x + -66 = 7 Reorder the terms: -66 + -2x + 2x2 = 7 Solving -66 + -2x + 2x2 = 7 Solving for variable 'x'. Reorder the terms: -66 + -7 + -2x + 2x2 = 7 + -7 Combine like terms: -66 + -7 = -73 -73 + -2x + 2x2 = 7 + -7 Combine like terms: 7 + -7 = 0 -73 + -2x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -36.5 + -1x + x2 = 0 Move the constant term to the right: Add '36.5' to each side of the equation. -36.5 + -1x + 36.5 + x2 = 0 + 36.5 Reorder the terms: -36.5 + 36.5 + -1x + x2 = 0 + 36.5 Combine like terms: -36.5 + 36.5 = 0.0 0.0 + -1x + x2 = 0 + 36.5 -1x + x2 = 0 + 36.5 Combine like terms: 0 + 36.5 = 36.5 -1x + x2 = 36.5 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = 36.5 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 36.5 + 0.25 Combine like terms: 36.5 + 0.25 = 36.75 0.25 + -1x + x2 = 36.75 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 36.75 Calculate the square root of the right side: 6.062177826 Break this problem into two subproblems by setting (x + -0.5) equal to 6.062177826 and -6.062177826.Subproblem 1
x + -0.5 = 6.062177826 Simplifying x + -0.5 = 6.062177826 Reorder the terms: -0.5 + x = 6.062177826 Solving -0.5 + x = 6.062177826 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 6.062177826 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 6.062177826 + 0.5 x = 6.062177826 + 0.5 Combine like terms: 6.062177826 + 0.5 = 6.562177826 x = 6.562177826 Simplifying x = 6.562177826Subproblem 2
x + -0.5 = -6.062177826 Simplifying x + -0.5 = -6.062177826 Reorder the terms: -0.5 + x = -6.062177826 Solving -0.5 + x = -6.062177826 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -6.062177826 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -6.062177826 + 0.5 x = -6.062177826 + 0.5 Combine like terms: -6.062177826 + 0.5 = -5.562177826 x = -5.562177826 Simplifying x = -5.562177826Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.562177826, -5.562177826}
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