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Simplifying x2 + -28x + -160 = 0 Reorder the terms: -160 + -28x + x2 = 0 Solving -160 + -28x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '160' to each side of the equation. -160 + -28x + 160 + x2 = 0 + 160 Reorder the terms: -160 + 160 + -28x + x2 = 0 + 160 Combine like terms: -160 + 160 = 0 0 + -28x + x2 = 0 + 160 -28x + x2 = 0 + 160 Combine like terms: 0 + 160 = 160 -28x + x2 = 160 The x term is -28x. Take half its coefficient (-14). Square it (196) and add it to both sides. Add '196' to each side of the equation. -28x + 196 + x2 = 160 + 196 Reorder the terms: 196 + -28x + x2 = 160 + 196 Combine like terms: 160 + 196 = 356 196 + -28x + x2 = 356 Factor a perfect square on the left side: (x + -14)(x + -14) = 356 Calculate the square root of the right side: 18.867962264 Break this problem into two subproblems by setting (x + -14) equal to 18.867962264 and -18.867962264.Subproblem 1
x + -14 = 18.867962264 Simplifying x + -14 = 18.867962264 Reorder the terms: -14 + x = 18.867962264 Solving -14 + x = 18.867962264 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '14' to each side of the equation. -14 + 14 + x = 18.867962264 + 14 Combine like terms: -14 + 14 = 0 0 + x = 18.867962264 + 14 x = 18.867962264 + 14 Combine like terms: 18.867962264 + 14 = 32.867962264 x = 32.867962264 Simplifying x = 32.867962264Subproblem 2
x + -14 = -18.867962264 Simplifying x + -14 = -18.867962264 Reorder the terms: -14 + x = -18.867962264 Solving -14 + x = -18.867962264 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '14' to each side of the equation. -14 + 14 + x = -18.867962264 + 14 Combine like terms: -14 + 14 = 0 0 + x = -18.867962264 + 14 x = -18.867962264 + 14 Combine like terms: -18.867962264 + 14 = -4.867962264 x = -4.867962264 Simplifying x = -4.867962264Solution
The solution to the problem is based on the solutions from the subproblems. x = {32.867962264, -4.867962264}
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