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Simplifying 8x2 + -46x + -15 = 0 Reorder the terms: -15 + -46x + 8x2 = 0 Solving -15 + -46x + 8x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -1.875 + -5.75x + x2 = 0 Move the constant term to the right: Add '1.875' to each side of the equation. -1.875 + -5.75x + 1.875 + x2 = 0 + 1.875 Reorder the terms: -1.875 + 1.875 + -5.75x + x2 = 0 + 1.875 Combine like terms: -1.875 + 1.875 = 0.000 0.000 + -5.75x + x2 = 0 + 1.875 -5.75x + x2 = 0 + 1.875 Combine like terms: 0 + 1.875 = 1.875 -5.75x + x2 = 1.875 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 = 1.875 + 8.265625 Reorder the terms: 8.265625 + -5.75x + x2 = 1.875 + 8.265625 Combine like terms: 1.875 + 8.265625 = 10.140625 8.265625 + -5.75x + x2 = 10.140625 Factor a perfect square on the left side: (x + -2.875)(x + -2.875) = 10.140625 Calculate the square root of the right side: 3.184434801 Break this problem into two subproblems by setting (x + -2.875) equal to 3.184434801 and -3.184434801.Subproblem 1
x + -2.875 = 3.184434801 Simplifying x + -2.875 = 3.184434801 Reorder the terms: -2.875 + x = 3.184434801 Solving -2.875 + x = 3.184434801 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 = 3.184434801 + 2.875 Combine like terms: -2.875 + 2.875 = 0.000 0.000 + x = 3.184434801 + 2.875 x = 3.184434801 + 2.875 Combine like terms: 3.184434801 + 2.875 = 6.059434801 x = 6.059434801 Simplifying x = 6.059434801Subproblem 2
x + -2.875 = -3.184434801 Simplifying x + -2.875 = -3.184434801 Reorder the terms: -2.875 + x = -3.184434801 Solving -2.875 + x = -3.184434801 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 = -3.184434801 + 2.875 Combine like terms: -2.875 + 2.875 = 0.000 0.000 + x = -3.184434801 + 2.875 x = -3.184434801 + 2.875 Combine like terms: -3.184434801 + 2.875 = -0.309434801 x = -0.309434801 Simplifying x = -0.309434801Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.059434801, -0.309434801}
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