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Simplifying x2 + -16x = -7 Reorder the terms: -16x + x2 = -7 Solving -16x + x2 = -7 Solving for variable 'x'. Reorder the terms: 7 + -16x + x2 = -7 + 7 Combine like terms: -7 + 7 = 0 7 + -16x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-7' to each side of the equation. 7 + -16x + -7 + x2 = 0 + -7 Reorder the terms: 7 + -7 + -16x + x2 = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -16x + x2 = 0 + -7 -16x + x2 = 0 + -7 Combine like terms: 0 + -7 = -7 -16x + x2 = -7 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 = -7 + 64 Reorder the terms: 64 + -16x + x2 = -7 + 64 Combine like terms: -7 + 64 = 57 64 + -16x + x2 = 57 Factor a perfect square on the left side: (x + -8)(x + -8) = 57 Calculate the square root of the right side: 7.549834435 Break this problem into two subproblems by setting (x + -8) equal to 7.549834435 and -7.549834435.Subproblem 1
x + -8 = 7.549834435 Simplifying x + -8 = 7.549834435 Reorder the terms: -8 + x = 7.549834435 Solving -8 + x = 7.549834435 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 = 7.549834435 + 8 Combine like terms: -8 + 8 = 0 0 + x = 7.549834435 + 8 x = 7.549834435 + 8 Combine like terms: 7.549834435 + 8 = 15.549834435 x = 15.549834435 Simplifying x = 15.549834435Subproblem 2
x + -8 = -7.549834435 Simplifying x + -8 = -7.549834435 Reorder the terms: -8 + x = -7.549834435 Solving -8 + x = -7.549834435 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 = -7.549834435 + 8 Combine like terms: -8 + 8 = 0 0 + x = -7.549834435 + 8 x = -7.549834435 + 8 Combine like terms: -7.549834435 + 8 = 0.450165565 x = 0.450165565 Simplifying x = 0.450165565Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.549834435, 0.450165565}
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