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Simplifying x2 + -16x + 53 = 0 Reorder the terms: 53 + -16x + x2 = 0 Solving 53 + -16x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-53' to each side of the equation. 53 + -16x + -53 + x2 = 0 + -53 Reorder the terms: 53 + -53 + -16x + x2 = 0 + -53 Combine like terms: 53 + -53 = 0 0 + -16x + x2 = 0 + -53 -16x + x2 = 0 + -53 Combine like terms: 0 + -53 = -53 -16x + x2 = -53 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 = -53 + 64 Reorder the terms: 64 + -16x + x2 = -53 + 64 Combine like terms: -53 + 64 = 11 64 + -16x + x2 = 11 Factor a perfect square on the left side: (x + -8)(x + -8) = 11 Calculate the square root of the right side: 3.31662479 Break this problem into two subproblems by setting (x + -8) equal to 3.31662479 and -3.31662479.Subproblem 1
x + -8 = 3.31662479 Simplifying x + -8 = 3.31662479 Reorder the terms: -8 + x = 3.31662479 Solving -8 + x = 3.31662479 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 = 3.31662479 + 8 Combine like terms: -8 + 8 = 0 0 + x = 3.31662479 + 8 x = 3.31662479 + 8 Combine like terms: 3.31662479 + 8 = 11.31662479 x = 11.31662479 Simplifying x = 11.31662479Subproblem 2
x + -8 = -3.31662479 Simplifying x + -8 = -3.31662479 Reorder the terms: -8 + x = -3.31662479 Solving -8 + x = -3.31662479 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 = -3.31662479 + 8 Combine like terms: -8 + 8 = 0 0 + x = -3.31662479 + 8 x = -3.31662479 + 8 Combine like terms: -3.31662479 + 8 = 4.68337521 x = 4.68337521 Simplifying x = 4.68337521Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.31662479, 4.68337521}
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