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Simplifying -28 + x2 + -16x = 0 Reorder the terms: -28 + -16x + x2 = 0 Solving -28 + -16x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '28' to each side of the equation. -28 + -16x + 28 + x2 = 0 + 28 Reorder the terms: -28 + 28 + -16x + x2 = 0 + 28 Combine like terms: -28 + 28 = 0 0 + -16x + x2 = 0 + 28 -16x + x2 = 0 + 28 Combine like terms: 0 + 28 = 28 -16x + x2 = 28 The x term is -16x. Take half its coefficient (-8). Square it (64) and add it to both sides. Add '64' to each side of the equation. -16x + 64 + x2 = 28 + 64 Reorder the terms: 64 + -16x + x2 = 28 + 64 Combine like terms: 28 + 64 = 92 64 + -16x + x2 = 92 Factor a perfect square on the left side: (x + -8)(x + -8) = 92 Calculate the square root of the right side: 9.591663047 Break this problem into two subproblems by setting (x + -8) equal to 9.591663047 and -9.591663047.Subproblem 1
x + -8 = 9.591663047 Simplifying x + -8 = 9.591663047 Reorder the terms: -8 + x = 9.591663047 Solving -8 + x = 9.591663047 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + x = 9.591663047 + 8 Combine like terms: -8 + 8 = 0 0 + x = 9.591663047 + 8 x = 9.591663047 + 8 Combine like terms: 9.591663047 + 8 = 17.591663047 x = 17.591663047 Simplifying x = 17.591663047Subproblem 2
x + -8 = -9.591663047 Simplifying x + -8 = -9.591663047 Reorder the terms: -8 + x = -9.591663047 Solving -8 + x = -9.591663047 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + x = -9.591663047 + 8 Combine like terms: -8 + 8 = 0 0 + x = -9.591663047 + 8 x = -9.591663047 + 8 Combine like terms: -9.591663047 + 8 = -1.591663047 x = -1.591663047 Simplifying x = -1.591663047Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.591663047, -1.591663047}
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