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Simplifying 300x2 + -342x + 61.56 = 0 Reorder the terms: 61.56 + -342x + 300x2 = 0 Solving 61.56 + -342x + 300x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 300 the coefficient of the squared term: Divide each side by '300'. 0.2052 + -1.14x + x2 = 0 Move the constant term to the right: Add '-0.2052' to each side of the equation. 0.2052 + -1.14x + -0.2052 + x2 = 0 + -0.2052 Reorder the terms: 0.2052 + -0.2052 + -1.14x + x2 = 0 + -0.2052 Combine like terms: 0.2052 + -0.2052 = 0.0000 0.0000 + -1.14x + x2 = 0 + -0.2052 -1.14x + x2 = 0 + -0.2052 Combine like terms: 0 + -0.2052 = -0.2052 -1.14x + x2 = -0.2052 The x term is -1.14x. Take half its coefficient (-0.57). Square it (0.3249) and add it to both sides. Add '0.3249' to each side of the equation. -1.14x + 0.3249 + x2 = -0.2052 + 0.3249 Reorder the terms: 0.3249 + -1.14x + x2 = -0.2052 + 0.3249 Combine like terms: -0.2052 + 0.3249 = 0.1197 0.3249 + -1.14x + x2 = 0.1197 Factor a perfect square on the left side: (x + -0.57)(x + -0.57) = 0.1197 Calculate the square root of the right side: 0.345976878 Break this problem into two subproblems by setting (x + -0.57) equal to 0.345976878 and -0.345976878.Subproblem 1
x + -0.57 = 0.345976878 Simplifying x + -0.57 = 0.345976878 Reorder the terms: -0.57 + x = 0.345976878 Solving -0.57 + x = 0.345976878 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.57' to each side of the equation. -0.57 + 0.57 + x = 0.345976878 + 0.57 Combine like terms: -0.57 + 0.57 = 0.00 0.00 + x = 0.345976878 + 0.57 x = 0.345976878 + 0.57 Combine like terms: 0.345976878 + 0.57 = 0.915976878 x = 0.915976878 Simplifying x = 0.915976878Subproblem 2
x + -0.57 = -0.345976878 Simplifying x + -0.57 = -0.345976878 Reorder the terms: -0.57 + x = -0.345976878 Solving -0.57 + x = -0.345976878 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.57' to each side of the equation. -0.57 + 0.57 + x = -0.345976878 + 0.57 Combine like terms: -0.57 + 0.57 = 0.00 0.00 + x = -0.345976878 + 0.57 x = -0.345976878 + 0.57 Combine like terms: -0.345976878 + 0.57 = 0.224023122 x = 0.224023122 Simplifying x = 0.224023122Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.915976878, 0.224023122}
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