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Simplifying X2 + -3X + -8 = 76 Reorder the terms: -8 + -3X + X2 = 76 Solving -8 + -3X + X2 = 76 Solving for variable 'X'. Reorder the terms: -8 + -76 + -3X + X2 = 76 + -76 Combine like terms: -8 + -76 = -84 -84 + -3X + X2 = 76 + -76 Combine like terms: 76 + -76 = 0 -84 + -3X + X2 = 0 Begin completing the square. Move the constant term to the right: Add '84' to each side of the equation. -84 + -3X + 84 + X2 = 0 + 84 Reorder the terms: -84 + 84 + -3X + X2 = 0 + 84 Combine like terms: -84 + 84 = 0 0 + -3X + X2 = 0 + 84 -3X + X2 = 0 + 84 Combine like terms: 0 + 84 = 84 -3X + X2 = 84 The X term is -3X. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3X + 2.25 + X2 = 84 + 2.25 Reorder the terms: 2.25 + -3X + X2 = 84 + 2.25 Combine like terms: 84 + 2.25 = 86.25 2.25 + -3X + X2 = 86.25 Factor a perfect square on the left side: (X + -1.5)(X + -1.5) = 86.25 Calculate the square root of the right side: 9.287087811 Break this problem into two subproblems by setting (X + -1.5) equal to 9.287087811 and -9.287087811.Subproblem 1
X + -1.5 = 9.287087811 Simplifying X + -1.5 = 9.287087811 Reorder the terms: -1.5 + X = 9.287087811 Solving -1.5 + X = 9.287087811 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + X = 9.287087811 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + X = 9.287087811 + 1.5 X = 9.287087811 + 1.5 Combine like terms: 9.287087811 + 1.5 = 10.787087811 X = 10.787087811 Simplifying X = 10.787087811Subproblem 2
X + -1.5 = -9.287087811 Simplifying X + -1.5 = -9.287087811 Reorder the terms: -1.5 + X = -9.287087811 Solving -1.5 + X = -9.287087811 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + X = -9.287087811 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + X = -9.287087811 + 1.5 X = -9.287087811 + 1.5 Combine like terms: -9.287087811 + 1.5 = -7.787087811 X = -7.787087811 Simplifying X = -7.787087811Solution
The solution to the problem is based on the solutions from the subproblems. X = {10.787087811, -7.787087811}
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