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Simplifying 2x2 + -28x + 83 = 0 Reorder the terms: 83 + -28x + 2x2 = 0 Solving 83 + -28x + 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'. 41.5 + -14x + x2 = 0 Move the constant term to the right: Add '-41.5' to each side of the equation. 41.5 + -14x + -41.5 + x2 = 0 + -41.5 Reorder the terms: 41.5 + -41.5 + -14x + x2 = 0 + -41.5 Combine like terms: 41.5 + -41.5 = 0.0 0.0 + -14x + x2 = 0 + -41.5 -14x + x2 = 0 + -41.5 Combine like terms: 0 + -41.5 = -41.5 -14x + x2 = -41.5 The x term is -14x. Take half its coefficient (-7). Square it (49) and add it to both sides. Add '49' to each side of the equation. -14x + 49 + x2 = -41.5 + 49 Reorder the terms: 49 + -14x + x2 = -41.5 + 49 Combine like terms: -41.5 + 49 = 7.5 49 + -14x + x2 = 7.5 Factor a perfect square on the left side: (x + -7)(x + -7) = 7.5 Calculate the square root of the right side: 2.738612788 Break this problem into two subproblems by setting (x + -7) equal to 2.738612788 and -2.738612788.Subproblem 1
x + -7 = 2.738612788 Simplifying x + -7 = 2.738612788 Reorder the terms: -7 + x = 2.738612788 Solving -7 + x = 2.738612788 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + x = 2.738612788 + 7 Combine like terms: -7 + 7 = 0 0 + x = 2.738612788 + 7 x = 2.738612788 + 7 Combine like terms: 2.738612788 + 7 = 9.738612788 x = 9.738612788 Simplifying x = 9.738612788Subproblem 2
x + -7 = -2.738612788 Simplifying x + -7 = -2.738612788 Reorder the terms: -7 + x = -2.738612788 Solving -7 + x = -2.738612788 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + x = -2.738612788 + 7 Combine like terms: -7 + 7 = 0 0 + x = -2.738612788 + 7 x = -2.738612788 + 7 Combine like terms: -2.738612788 + 7 = 4.261387212 x = 4.261387212 Simplifying x = 4.261387212Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.738612788, 4.261387212}
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