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Simplifying 5x2 + -5x + 0.8 = 0 Reorder the terms: 0.8 + -5x + 5x2 = 0 Solving 0.8 + -5x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 0.16 + -1x + x2 = 0 Move the constant term to the right: Add '-0.16' to each side of the equation. 0.16 + -1x + -0.16 + x2 = 0 + -0.16 Reorder the terms: 0.16 + -0.16 + -1x + x2 = 0 + -0.16 Combine like terms: 0.16 + -0.16 = 0.00 0.00 + -1x + x2 = 0 + -0.16 -1x + x2 = 0 + -0.16 Combine like terms: 0 + -0.16 = -0.16 -1x + x2 = -0.16 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 = -0.16 + 0.25 Reorder the terms: 0.25 + -1x + x2 = -0.16 + 0.25 Combine like terms: -0.16 + 0.25 = 0.09 0.25 + -1x + x2 = 0.09 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 0.09 Calculate the square root of the right side: 0.3 Break this problem into two subproblems by setting (x + -0.5) equal to 0.3 and -0.3.Subproblem 1
x + -0.5 = 0.3 Simplifying x + -0.5 = 0.3 Reorder the terms: -0.5 + x = 0.3 Solving -0.5 + x = 0.3 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 = 0.3 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 0.3 + 0.5 x = 0.3 + 0.5 Combine like terms: 0.3 + 0.5 = 0.8 x = 0.8 Simplifying x = 0.8Subproblem 2
x + -0.5 = -0.3 Simplifying x + -0.5 = -0.3 Reorder the terms: -0.5 + x = -0.3 Solving -0.5 + x = -0.3 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 = -0.3 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -0.3 + 0.5 x = -0.3 + 0.5 Combine like terms: -0.3 + 0.5 = 0.2 x = 0.2 Simplifying x = 0.2Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.8, 0.2}
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