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Simplifying 171 + -8x = 108 + 5x2 Solving 171 + -8x = 108 + 5x2 Solving for variable 'x'. Reorder the terms: 171 + -108 + -8x + -5x2 = 108 + 5x2 + -108 + -5x2 Combine like terms: 171 + -108 = 63 63 + -8x + -5x2 = 108 + 5x2 + -108 + -5x2 Reorder the terms: 63 + -8x + -5x2 = 108 + -108 + 5x2 + -5x2 Combine like terms: 108 + -108 = 0 63 + -8x + -5x2 = 0 + 5x2 + -5x2 63 + -8x + -5x2 = 5x2 + -5x2 Combine like terms: 5x2 + -5x2 = 0 63 + -8x + -5x2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -12.6 + 1.6x + x2 = 0 Move the constant term to the right: Add '12.6' to each side of the equation. -12.6 + 1.6x + 12.6 + x2 = 0 + 12.6 Reorder the terms: -12.6 + 12.6 + 1.6x + x2 = 0 + 12.6 Combine like terms: -12.6 + 12.6 = 0.0 0.0 + 1.6x + x2 = 0 + 12.6 1.6x + x2 = 0 + 12.6 Combine like terms: 0 + 12.6 = 12.6 1.6x + x2 = 12.6 The x term is 1.6x. Take half its coefficient (0.8). Square it (0.64) and add it to both sides. Add '0.64' to each side of the equation. 1.6x + 0.64 + x2 = 12.6 + 0.64 Reorder the terms: 0.64 + 1.6x + x2 = 12.6 + 0.64 Combine like terms: 12.6 + 0.64 = 13.24 0.64 + 1.6x + x2 = 13.24 Factor a perfect square on the left side: (x + 0.8)(x + 0.8) = 13.24 Calculate the square root of the right side: 3.63868108 Break this problem into two subproblems by setting (x + 0.8) equal to 3.63868108 and -3.63868108.Subproblem 1
x + 0.8 = 3.63868108 Simplifying x + 0.8 = 3.63868108 Reorder the terms: 0.8 + x = 3.63868108 Solving 0.8 + x = 3.63868108 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8' to each side of the equation. 0.8 + -0.8 + x = 3.63868108 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + x = 3.63868108 + -0.8 x = 3.63868108 + -0.8 Combine like terms: 3.63868108 + -0.8 = 2.83868108 x = 2.83868108 Simplifying x = 2.83868108Subproblem 2
x + 0.8 = -3.63868108 Simplifying x + 0.8 = -3.63868108 Reorder the terms: 0.8 + x = -3.63868108 Solving 0.8 + x = -3.63868108 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8' to each side of the equation. 0.8 + -0.8 + x = -3.63868108 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + x = -3.63868108 + -0.8 x = -3.63868108 + -0.8 Combine like terms: -3.63868108 + -0.8 = -4.43868108 x = -4.43868108 Simplifying x = -4.43868108Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.83868108, -4.43868108}
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