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Simplifying 1.829 = -4.9x2 + 4.9x + 0.8 Reorder the terms: 1.829 = 0.8 + 4.9x + -4.9x2 Solving 1.829 = 0.8 + 4.9x + -4.9x2 Solving for variable 'x'. Combine like terms: 1.829 + -0.8 = 1.029 1.029 + -4.9x + 4.9x2 = 0.8 + 4.9x + -4.9x2 + -0.8 + -4.9x + 4.9x2 Reorder the terms: 1.029 + -4.9x + 4.9x2 = 0.8 + -0.8 + 4.9x + -4.9x + -4.9x2 + 4.9x2 Combine like terms: 0.8 + -0.8 = 0.0 1.029 + -4.9x + 4.9x2 = 0.0 + 4.9x + -4.9x + -4.9x2 + 4.9x2 1.029 + -4.9x + 4.9x2 = 4.9x + -4.9x + -4.9x2 + 4.9x2 Combine like terms: 4.9x + -4.9x = 0.0 1.029 + -4.9x + 4.9x2 = 0.0 + -4.9x2 + 4.9x2 1.029 + -4.9x + 4.9x2 = -4.9x2 + 4.9x2 Combine like terms: -4.9x2 + 4.9x2 = 0.0 1.029 + -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'. 0.21 + -1x + x2 = 0 Move the constant term to the right: Add '-0.21' to each side of the equation. 0.21 + -1x + -0.21 + x2 = 0 + -0.21 Reorder the terms: 0.21 + -0.21 + -1x + x2 = 0 + -0.21 Combine like terms: 0.21 + -0.21 = 0.00 0.00 + -1x + x2 = 0 + -0.21 -1x + x2 = 0 + -0.21 Combine like terms: 0 + -0.21 = -0.21 -1x + x2 = -0.21 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 = -0.21 + 0.25 Reorder the terms: 0.25 + -1x + x2 = -0.21 + 0.25 Combine like terms: -0.21 + 0.25 = 0.04 0.25 + -1x + x2 = 0.04 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 0.04 Calculate the square root of the right side: 0.2 Break this problem into two subproblems by setting (x + -0.5) equal to 0.2 and -0.2.Subproblem 1
x + -0.5 = 0.2 Simplifying x + -0.5 = 0.2 Reorder the terms: -0.5 + x = 0.2 Solving -0.5 + x = 0.2 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 = 0.2 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 0.2 + 0.5 x = 0.2 + 0.5 Combine like terms: 0.2 + 0.5 = 0.7 x = 0.7 Simplifying x = 0.7Subproblem 2
x + -0.5 = -0.2 Simplifying x + -0.5 = -0.2 Reorder the terms: -0.5 + x = -0.2 Solving -0.5 + x = -0.2 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 = -0.2 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -0.2 + 0.5 x = -0.2 + 0.5 Combine like terms: -0.2 + 0.5 = 0.3 x = 0.3 Simplifying x = 0.3Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.7, 0.3}
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