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Simplifying x2 + -1x + -48 = 16 Reorder the terms: -48 + -1x + x2 = 16 Solving -48 + -1x + x2 = 16 Solving for variable 'x'. Reorder the terms: -48 + -16 + -1x + x2 = 16 + -16 Combine like terms: -48 + -16 = -64 -64 + -1x + x2 = 16 + -16 Combine like terms: 16 + -16 = 0 -64 + -1x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '64' to each side of the equation. -64 + -1x + 64 + x2 = 0 + 64 Reorder the terms: -64 + 64 + -1x + x2 = 0 + 64 Combine like terms: -64 + 64 = 0 0 + -1x + x2 = 0 + 64 -1x + x2 = 0 + 64 Combine like terms: 0 + 64 = 64 -1x + x2 = 64 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = 64 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 64 + 0.25 Combine like terms: 64 + 0.25 = 64.25 0.25 + -1x + x2 = 64.25 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 64.25 Calculate the square root of the right side: 8.015609771 Break this problem into two subproblems by setting (x + -0.5) equal to 8.015609771 and -8.015609771.Subproblem 1
x + -0.5 = 8.015609771 Simplifying x + -0.5 = 8.015609771 Reorder the terms: -0.5 + x = 8.015609771 Solving -0.5 + x = 8.015609771 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 8.015609771 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 8.015609771 + 0.5 x = 8.015609771 + 0.5 Combine like terms: 8.015609771 + 0.5 = 8.515609771 x = 8.515609771 Simplifying x = 8.515609771Subproblem 2
x + -0.5 = -8.015609771 Simplifying x + -0.5 = -8.015609771 Reorder the terms: -0.5 + x = -8.015609771 Solving -0.5 + x = -8.015609771 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -8.015609771 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -8.015609771 + 0.5 x = -8.015609771 + 0.5 Combine like terms: -8.015609771 + 0.5 = -7.515609771 x = -7.515609771 Simplifying x = -7.515609771Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.515609771, -7.515609771}
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