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Simplifying 16x2 + 2 + 2x + -15x2 + -1 + 14x = 0 Reorder the terms: 2 + -1 + 2x + 14x + 16x2 + -15x2 = 0 Combine like terms: 2 + -1 = 1 1 + 2x + 14x + 16x2 + -15x2 = 0 Combine like terms: 2x + 14x = 16x 1 + 16x + 16x2 + -15x2 = 0 Combine like terms: 16x2 + -15x2 = 1x2 1 + 16x + 1x2 = 0 Solving 1 + 16x + 1x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-1' to each side of the equation. 1 + 16x + -1 + x2 = 0 + -1 Reorder the terms: 1 + -1 + 16x + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 16x + x2 = 0 + -1 16x + x2 = 0 + -1 Combine like terms: 0 + -1 = -1 16x + x2 = -1 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 = -1 + 64 Reorder the terms: 64 + 16x + x2 = -1 + 64 Combine like terms: -1 + 64 = 63 64 + 16x + x2 = 63 Factor a perfect square on the left side: (x + 8)(x + 8) = 63 Calculate the square root of the right side: 7.937253933 Break this problem into two subproblems by setting (x + 8) equal to 7.937253933 and -7.937253933.Subproblem 1
x + 8 = 7.937253933 Simplifying x + 8 = 7.937253933 Reorder the terms: 8 + x = 7.937253933 Solving 8 + x = 7.937253933 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 = 7.937253933 + -8 Combine like terms: 8 + -8 = 0 0 + x = 7.937253933 + -8 x = 7.937253933 + -8 Combine like terms: 7.937253933 + -8 = -0.062746067 x = -0.062746067 Simplifying x = -0.062746067Subproblem 2
x + 8 = -7.937253933 Simplifying x + 8 = -7.937253933 Reorder the terms: 8 + x = -7.937253933 Solving 8 + x = -7.937253933 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 = -7.937253933 + -8 Combine like terms: 8 + -8 = 0 0 + x = -7.937253933 + -8 x = -7.937253933 + -8 Combine like terms: -7.937253933 + -8 = -15.937253933 x = -15.937253933 Simplifying x = -15.937253933Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.062746067, -15.937253933}
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