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Simplifying 0.45x2 + 11.7x = 101.4 Reorder the terms: 11.7x + 0.45x2 = 101.4 Solving 11.7x + 0.45x2 = 101.4 Solving for variable 'x'. Reorder the terms: -101.4 + 11.7x + 0.45x2 = 101.4 + -101.4 Combine like terms: 101.4 + -101.4 = 0.0 -101.4 + 11.7x + 0.45x2 = 0.0 Begin completing the square. Divide all terms by 0.45 the coefficient of the squared term: Divide each side by '0.45'. -225.3333333 + 26x + x2 = 0 Move the constant term to the right: Add '225.3333333' to each side of the equation. -225.3333333 + 26x + 225.3333333 + x2 = 0 + 225.3333333 Reorder the terms: -225.3333333 + 225.3333333 + 26x + x2 = 0 + 225.3333333 Combine like terms: -225.3333333 + 225.3333333 = 0.0000000 0.0000000 + 26x + x2 = 0 + 225.3333333 26x + x2 = 0 + 225.3333333 Combine like terms: 0 + 225.3333333 = 225.3333333 26x + x2 = 225.3333333 The x term is 26x. Take half its coefficient (13). Square it (169) and add it to both sides. Add '169' to each side of the equation. 26x + 169 + x2 = 225.3333333 + 169 Reorder the terms: 169 + 26x + x2 = 225.3333333 + 169 Combine like terms: 225.3333333 + 169 = 394.3333333 169 + 26x + x2 = 394.3333333 Factor a perfect square on the left side: (x + 13)(x + 13) = 394.3333333 Calculate the square root of the right side: 19.857828011 Break this problem into two subproblems by setting (x + 13) equal to 19.857828011 and -19.857828011.Subproblem 1
x + 13 = 19.857828011 Simplifying x + 13 = 19.857828011 Reorder the terms: 13 + x = 19.857828011 Solving 13 + x = 19.857828011 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + x = 19.857828011 + -13 Combine like terms: 13 + -13 = 0 0 + x = 19.857828011 + -13 x = 19.857828011 + -13 Combine like terms: 19.857828011 + -13 = 6.857828011 x = 6.857828011 Simplifying x = 6.857828011Subproblem 2
x + 13 = -19.857828011 Simplifying x + 13 = -19.857828011 Reorder the terms: 13 + x = -19.857828011 Solving 13 + x = -19.857828011 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + x = -19.857828011 + -13 Combine like terms: 13 + -13 = 0 0 + x = -19.857828011 + -13 x = -19.857828011 + -13 Combine like terms: -19.857828011 + -13 = -32.857828011 x = -32.857828011 Simplifying x = -32.857828011Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.857828011, -32.857828011}
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