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Simplifying -8x2 + 46x + -30 = 17 Reorder the terms: -30 + 46x + -8x2 = 17 Solving -30 + 46x + -8x2 = 17 Solving for variable 'x'. Reorder the terms: -30 + -17 + 46x + -8x2 = 17 + -17 Combine like terms: -30 + -17 = -47 -47 + 46x + -8x2 = 17 + -17 Combine like terms: 17 + -17 = 0 -47 + 46x + -8x2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. 5.875 + -5.75x + x2 = 0 Move the constant term to the right: Add '-5.875' to each side of the equation. 5.875 + -5.75x + -5.875 + x2 = 0 + -5.875 Reorder the terms: 5.875 + -5.875 + -5.75x + x2 = 0 + -5.875 Combine like terms: 5.875 + -5.875 = 0.000 0.000 + -5.75x + x2 = 0 + -5.875 -5.75x + x2 = 0 + -5.875 Combine like terms: 0 + -5.875 = -5.875 -5.75x + x2 = -5.875 The x term is -5.75x. Take half its coefficient (-2.875). Square it (8.265625) and add it to both sides. Add '8.265625' to each side of the equation. -5.75x + 8.265625 + x2 = -5.875 + 8.265625 Reorder the terms: 8.265625 + -5.75x + x2 = -5.875 + 8.265625 Combine like terms: -5.875 + 8.265625 = 2.390625 8.265625 + -5.75x + x2 = 2.390625 Factor a perfect square on the left side: (x + -2.875)(x + -2.875) = 2.390625 Calculate the square root of the right side: 1.54616461 Break this problem into two subproblems by setting (x + -2.875) equal to 1.54616461 and -1.54616461.Subproblem 1
x + -2.875 = 1.54616461 Simplifying x + -2.875 = 1.54616461 Reorder the terms: -2.875 + x = 1.54616461 Solving -2.875 + x = 1.54616461 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.875' to each side of the equation. -2.875 + 2.875 + x = 1.54616461 + 2.875 Combine like terms: -2.875 + 2.875 = 0.000 0.000 + x = 1.54616461 + 2.875 x = 1.54616461 + 2.875 Combine like terms: 1.54616461 + 2.875 = 4.42116461 x = 4.42116461 Simplifying x = 4.42116461Subproblem 2
x + -2.875 = -1.54616461 Simplifying x + -2.875 = -1.54616461 Reorder the terms: -2.875 + x = -1.54616461 Solving -2.875 + x = -1.54616461 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.875' to each side of the equation. -2.875 + 2.875 + x = -1.54616461 + 2.875 Combine like terms: -2.875 + 2.875 = 0.000 0.000 + x = -1.54616461 + 2.875 x = -1.54616461 + 2.875 Combine like terms: -1.54616461 + 2.875 = 1.32883539 x = 1.32883539 Simplifying x = 1.32883539Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.42116461, 1.32883539}
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