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Simplifying (x)(x) + 16x + 53 = 0 Multiply x * x 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 = -4.68337521 x = -4.68337521 Simplifying x = -4.68337521Subproblem 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 = -11.31662479 x = -11.31662479 Simplifying x = -11.31662479Solution
The solution to the problem is based on the solutions from the subproblems. x = {-4.68337521, -11.31662479}
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