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Simplifying 50x2 + -110x = -59.5 Reorder the terms: -110x + 50x2 = -59.5 Solving -110x + 50x2 = -59.5 Solving for variable 'x'. Reorder the terms: 59.5 + -110x + 50x2 = -59.5 + 59.5 Combine like terms: -59.5 + 59.5 = 0.0 59.5 + -110x + 50x2 = 0.0 Begin completing the square. Divide all terms by 50 the coefficient of the squared term: Divide each side by '50'. 1.19 + -2.2x + x2 = 0.0 Move the constant term to the right: Add '-1.19' to each side of the equation. 1.19 + -2.2x + -1.19 + x2 = 0.0 + -1.19 Reorder the terms: 1.19 + -1.19 + -2.2x + x2 = 0.0 + -1.19 Combine like terms: 1.19 + -1.19 = 0.00 0.00 + -2.2x + x2 = 0.0 + -1.19 -2.2x + x2 = 0.0 + -1.19 Combine like terms: 0.0 + -1.19 = -1.19 -2.2x + x2 = -1.19 The x term is -2.2x. Take half its coefficient (-1.1). Square it (1.21) and add it to both sides. Add '1.21' to each side of the equation. -2.2x + 1.21 + x2 = -1.19 + 1.21 Reorder the terms: 1.21 + -2.2x + x2 = -1.19 + 1.21 Combine like terms: -1.19 + 1.21 = 0.02 1.21 + -2.2x + x2 = 0.02 Factor a perfect square on the left side: (x + -1.1)(x + -1.1) = 0.02 Calculate the square root of the right side: 0.141421356 Break this problem into two subproblems by setting (x + -1.1) equal to 0.141421356 and -0.141421356.Subproblem 1
x + -1.1 = 0.141421356 Simplifying x + -1.1 = 0.141421356 Reorder the terms: -1.1 + x = 0.141421356 Solving -1.1 + x = 0.141421356 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.1' to each side of the equation. -1.1 + 1.1 + x = 0.141421356 + 1.1 Combine like terms: -1.1 + 1.1 = 0.0 0.0 + x = 0.141421356 + 1.1 x = 0.141421356 + 1.1 Combine like terms: 0.141421356 + 1.1 = 1.241421356 x = 1.241421356 Simplifying x = 1.241421356Subproblem 2
x + -1.1 = -0.141421356 Simplifying x + -1.1 = -0.141421356 Reorder the terms: -1.1 + x = -0.141421356 Solving -1.1 + x = -0.141421356 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.1' to each side of the equation. -1.1 + 1.1 + x = -0.141421356 + 1.1 Combine like terms: -1.1 + 1.1 = 0.0 0.0 + x = -0.141421356 + 1.1 x = -0.141421356 + 1.1 Combine like terms: -0.141421356 + 1.1 = 0.958578644 x = 0.958578644 Simplifying x = 0.958578644Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.241421356, 0.958578644}
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