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Simplifying x2 + -16x = 10 Reorder the terms: -16x + x2 = 10 Solving -16x + x2 = 10 Solving for variable 'x'. Reorder the terms: -10 + -16x + x2 = 10 + -10 Combine like terms: 10 + -10 = 0 -10 + -16x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '10' to each side of the equation. -10 + -16x + 10 + x2 = 0 + 10 Reorder the terms: -10 + 10 + -16x + x2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + -16x + x2 = 0 + 10 -16x + x2 = 0 + 10 Combine like terms: 0 + 10 = 10 -16x + x2 = 10 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 = 10 + 64 Reorder the terms: 64 + -16x + x2 = 10 + 64 Combine like terms: 10 + 64 = 74 64 + -16x + x2 = 74 Factor a perfect square on the left side: (x + -8)(x + -8) = 74 Calculate the square root of the right side: 8.602325267 Break this problem into two subproblems by setting (x + -8) equal to 8.602325267 and -8.602325267.Subproblem 1
x + -8 = 8.602325267 Simplifying x + -8 = 8.602325267 Reorder the terms: -8 + x = 8.602325267 Solving -8 + x = 8.602325267 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 = 8.602325267 + 8 Combine like terms: -8 + 8 = 0 0 + x = 8.602325267 + 8 x = 8.602325267 + 8 Combine like terms: 8.602325267 + 8 = 16.602325267 x = 16.602325267 Simplifying x = 16.602325267Subproblem 2
x + -8 = -8.602325267 Simplifying x + -8 = -8.602325267 Reorder the terms: -8 + x = -8.602325267 Solving -8 + x = -8.602325267 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 = -8.602325267 + 8 Combine like terms: -8 + 8 = 0 0 + x = -8.602325267 + 8 x = -8.602325267 + 8 Combine like terms: -8.602325267 + 8 = -0.602325267 x = -0.602325267 Simplifying x = -0.602325267Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.602325267, -0.602325267}
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