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Simplifying -0.25x2 + -0.6x + 0.3 = 0 Reorder the terms: 0.3 + -0.6x + -0.25x2 = 0 Solving 0.3 + -0.6x + -0.25x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.25 the coefficient of the squared term: Divide each side by '-0.25'. -1.2 + 2.4x + x2 = 0 Move the constant term to the right: Add '1.2' to each side of the equation. -1.2 + 2.4x + 1.2 + x2 = 0 + 1.2 Reorder the terms: -1.2 + 1.2 + 2.4x + x2 = 0 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + 2.4x + x2 = 0 + 1.2 2.4x + x2 = 0 + 1.2 Combine like terms: 0 + 1.2 = 1.2 2.4x + x2 = 1.2 The x term is 2.4x. Take half its coefficient (1.2). Square it (1.44) and add it to both sides. Add '1.44' to each side of the equation. 2.4x + 1.44 + x2 = 1.2 + 1.44 Reorder the terms: 1.44 + 2.4x + x2 = 1.2 + 1.44 Combine like terms: 1.2 + 1.44 = 2.64 1.44 + 2.4x + x2 = 2.64 Factor a perfect square on the left side: (x + 1.2)(x + 1.2) = 2.64 Calculate the square root of the right side: 1.624807681 Break this problem into two subproblems by setting (x + 1.2) equal to 1.624807681 and -1.624807681.Subproblem 1
x + 1.2 = 1.624807681 Simplifying x + 1.2 = 1.624807681 Reorder the terms: 1.2 + x = 1.624807681 Solving 1.2 + x = 1.624807681 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.2' to each side of the equation. 1.2 + -1.2 + x = 1.624807681 + -1.2 Combine like terms: 1.2 + -1.2 = 0.0 0.0 + x = 1.624807681 + -1.2 x = 1.624807681 + -1.2 Combine like terms: 1.624807681 + -1.2 = 0.424807681 x = 0.424807681 Simplifying x = 0.424807681Subproblem 2
x + 1.2 = -1.624807681 Simplifying x + 1.2 = -1.624807681 Reorder the terms: 1.2 + x = -1.624807681 Solving 1.2 + x = -1.624807681 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.2' to each side of the equation. 1.2 + -1.2 + x = -1.624807681 + -1.2 Combine like terms: 1.2 + -1.2 = 0.0 0.0 + x = -1.624807681 + -1.2 x = -1.624807681 + -1.2 Combine like terms: -1.624807681 + -1.2 = -2.824807681 x = -2.824807681 Simplifying x = -2.824807681Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.424807681, -2.824807681}
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