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Simplifying x2 + -17x + 48 = 0 Reorder the terms: 48 + -17x + x2 = 0 Solving 48 + -17x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-48' to each side of the equation. 48 + -17x + -48 + x2 = 0 + -48 Reorder the terms: 48 + -48 + -17x + x2 = 0 + -48 Combine like terms: 48 + -48 = 0 0 + -17x + x2 = 0 + -48 -17x + x2 = 0 + -48 Combine like terms: 0 + -48 = -48 -17x + x2 = -48 The x term is -17x. Take half its coefficient (-8.5). Square it (72.25) and add it to both sides. Add '72.25' to each side of the equation. -17x + 72.25 + x2 = -48 + 72.25 Reorder the terms: 72.25 + -17x + x2 = -48 + 72.25 Combine like terms: -48 + 72.25 = 24.25 72.25 + -17x + x2 = 24.25 Factor a perfect square on the left side: (x + -8.5)(x + -8.5) = 24.25 Calculate the square root of the right side: 4.924428901 Break this problem into two subproblems by setting (x + -8.5) equal to 4.924428901 and -4.924428901.Subproblem 1
x + -8.5 = 4.924428901 Simplifying x + -8.5 = 4.924428901 Reorder the terms: -8.5 + x = 4.924428901 Solving -8.5 + x = 4.924428901 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.5' to each side of the equation. -8.5 + 8.5 + x = 4.924428901 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + x = 4.924428901 + 8.5 x = 4.924428901 + 8.5 Combine like terms: 4.924428901 + 8.5 = 13.424428901 x = 13.424428901 Simplifying x = 13.424428901Subproblem 2
x + -8.5 = -4.924428901 Simplifying x + -8.5 = -4.924428901 Reorder the terms: -8.5 + x = -4.924428901 Solving -8.5 + x = -4.924428901 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.5' to each side of the equation. -8.5 + 8.5 + x = -4.924428901 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + x = -4.924428901 + 8.5 x = -4.924428901 + 8.5 Combine like terms: -4.924428901 + 8.5 = 3.575571099 x = 3.575571099 Simplifying x = 3.575571099Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.424428901, 3.575571099}
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