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Simplifying 0.254 = (18 + x)(18 + 94 + x) Combine like terms: 18 + 94 = 112 0.254 = (18 + x)(112 + x) Multiply (18 + x) * (112 + x) 0.254 = (18(112 + x) + x(112 + x)) 0.254 = ((112 * 18 + x * 18) + x(112 + x)) 0.254 = ((2016 + 18x) + x(112 + x)) 0.254 = (2016 + 18x + (112 * x + x * x)) 0.254 = (2016 + 18x + (112x + x2)) Combine like terms: 18x + 112x = 130x 0.254 = (2016 + 130x + x2) Solving 0.254 = 2016 + 130x + x2 Solving for variable 'x'. Combine like terms: 0.254 + -2016 = -2015.746 -2015.746 + -130x + -1x2 = 2016 + 130x + x2 + -2016 + -130x + -1x2 Reorder the terms: -2015.746 + -130x + -1x2 = 2016 + -2016 + 130x + -130x + x2 + -1x2 Combine like terms: 2016 + -2016 = 0 -2015.746 + -130x + -1x2 = 0 + 130x + -130x + x2 + -1x2 -2015.746 + -130x + -1x2 = 130x + -130x + x2 + -1x2 Combine like terms: 130x + -130x = 0 -2015.746 + -130x + -1x2 = 0 + x2 + -1x2 -2015.746 + -130x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -2015.746 + -130x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 2015.746 + 130x + x2 = 0 Move the constant term to the right: Add '-2015.746' to each side of the equation. 2015.746 + 130x + -2015.746 + x2 = 0 + -2015.746 Reorder the terms: 2015.746 + -2015.746 + 130x + x2 = 0 + -2015.746 Combine like terms: 2015.746 + -2015.746 = 0.000 0.000 + 130x + x2 = 0 + -2015.746 130x + x2 = 0 + -2015.746 Combine like terms: 0 + -2015.746 = -2015.746 130x + x2 = -2015.746 The x term is 130x. Take half its coefficient (65). Square it (4225) and add it to both sides. Add '4225' to each side of the equation. 130x + 4225 + x2 = -2015.746 + 4225 Reorder the terms: 4225 + 130x + x2 = -2015.746 + 4225 Combine like terms: -2015.746 + 4225 = 2209.254 4225 + 130x + x2 = 2209.254 Factor a perfect square on the left side: (x + 65)(x + 65) = 2209.254 Calculate the square root of the right side: 47.00270205 Break this problem into two subproblems by setting (x + 65) equal to 47.00270205 and -47.00270205.Subproblem 1
x + 65 = 47.00270205 Simplifying x + 65 = 47.00270205 Reorder the terms: 65 + x = 47.00270205 Solving 65 + x = 47.00270205 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-65' to each side of the equation. 65 + -65 + x = 47.00270205 + -65 Combine like terms: 65 + -65 = 0 0 + x = 47.00270205 + -65 x = 47.00270205 + -65 Combine like terms: 47.00270205 + -65 = -17.99729795 x = -17.99729795 Simplifying x = -17.99729795Subproblem 2
x + 65 = -47.00270205 Simplifying x + 65 = -47.00270205 Reorder the terms: 65 + x = -47.00270205 Solving 65 + x = -47.00270205 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-65' to each side of the equation. 65 + -65 + x = -47.00270205 + -65 Combine like terms: 65 + -65 = 0 0 + x = -47.00270205 + -65 x = -47.00270205 + -65 Combine like terms: -47.00270205 + -65 = -112.00270205 x = -112.00270205 Simplifying x = -112.00270205Solution
The solution to the problem is based on the solutions from the subproblems. x = {-17.99729795, -112.00270205}
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