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Simplifying 5 = 10 + 4.9x + -4.9x2 Solving 5 = 10 + 4.9x + -4.9x2 Solving for variable 'x'. Combine like terms: 5 + -10 = -5 -5 + -4.9x + 4.9x2 = 10 + 4.9x + -4.9x2 + -10 + -4.9x + 4.9x2 Reorder the terms: -5 + -4.9x + 4.9x2 = 10 + -10 + 4.9x + -4.9x + -4.9x2 + 4.9x2 Combine like terms: 10 + -10 = 0 -5 + -4.9x + 4.9x2 = 0 + 4.9x + -4.9x + -4.9x2 + 4.9x2 -5 + -4.9x + 4.9x2 = 4.9x + -4.9x + -4.9x2 + 4.9x2 Combine like terms: 4.9x + -4.9x = 0.0 -5 + -4.9x + 4.9x2 = 0.0 + -4.9x2 + 4.9x2 -5 + -4.9x + 4.9x2 = -4.9x2 + 4.9x2 Combine like terms: -4.9x2 + 4.9x2 = 0.0 -5 + -4.9x + 4.9x2 = 0.0 Begin completing the square. Divide all terms by 4.9 the coefficient of the squared term: Divide each side by '4.9'. -1.020408163 + -1x + x2 = 0 Move the constant term to the right: Add '1.020408163' to each side of the equation. -1.020408163 + -1x + 1.020408163 + x2 = 0 + 1.020408163 Reorder the terms: -1.020408163 + 1.020408163 + -1x + x2 = 0 + 1.020408163 Combine like terms: -1.020408163 + 1.020408163 = 0.000000000 0.000000000 + -1x + x2 = 0 + 1.020408163 -1x + x2 = 0 + 1.020408163 Combine like terms: 0 + 1.020408163 = 1.020408163 -1x + x2 = 1.020408163 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = 1.020408163 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 1.020408163 + 0.25 Combine like terms: 1.020408163 + 0.25 = 1.270408163 0.25 + -1x + x2 = 1.270408163 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 1.270408163 Calculate the square root of the right side: 1.127123845 Break this problem into two subproblems by setting (x + -0.5) equal to 1.127123845 and -1.127123845.Subproblem 1
x + -0.5 = 1.127123845 Simplifying x + -0.5 = 1.127123845 Reorder the terms: -0.5 + x = 1.127123845 Solving -0.5 + x = 1.127123845 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 1.127123845 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 1.127123845 + 0.5 x = 1.127123845 + 0.5 Combine like terms: 1.127123845 + 0.5 = 1.627123845 x = 1.627123845 Simplifying x = 1.627123845Subproblem 2
x + -0.5 = -1.127123845 Simplifying x + -0.5 = -1.127123845 Reorder the terms: -0.5 + x = -1.127123845 Solving -0.5 + x = -1.127123845 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -1.127123845 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -1.127123845 + 0.5 x = -1.127123845 + 0.5 Combine like terms: -1.127123845 + 0.5 = -0.627123845 x = -0.627123845 Simplifying x = -0.627123845Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.627123845, -0.627123845}
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