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Simplifying 0.1x2 + -1x = -1.1x2 + 40 Reorder the terms: -1x + 0.1x2 = -1.1x2 + 40 Reorder the terms: -1x + 0.1x2 = 40 + -1.1x2 Solving -1x + 0.1x2 = 40 + -1.1x2 Solving for variable 'x'. Reorder the terms: -40 + -1x + 0.1x2 + 1.1x2 = 40 + -1.1x2 + -40 + 1.1x2 Combine like terms: 0.1x2 + 1.1x2 = 1.2x2 -40 + -1x + 1.2x2 = 40 + -1.1x2 + -40 + 1.1x2 Reorder the terms: -40 + -1x + 1.2x2 = 40 + -40 + -1.1x2 + 1.1x2 Combine like terms: 40 + -40 = 0 -40 + -1x + 1.2x2 = 0 + -1.1x2 + 1.1x2 -40 + -1x + 1.2x2 = -1.1x2 + 1.1x2 Combine like terms: -1.1x2 + 1.1x2 = 0.0 -40 + -1x + 1.2x2 = 0.0 Begin completing the square. Divide all terms by 1.2 the coefficient of the squared term: Divide each side by '1.2'. -33.33333333 + -0.8333333333x + x2 = 0 Move the constant term to the right: Add '33.33333333' to each side of the equation. -33.33333333 + -0.8333333333x + 33.33333333 + x2 = 0 + 33.33333333 Reorder the terms: -33.33333333 + 33.33333333 + -0.8333333333x + x2 = 0 + 33.33333333 Combine like terms: -33.33333333 + 33.33333333 = 0.00000000 0.00000000 + -0.8333333333x + x2 = 0 + 33.33333333 -0.8333333333x + x2 = 0 + 33.33333333 Combine like terms: 0 + 33.33333333 = 33.33333333 -0.8333333333x + x2 = 33.33333333 The x term is -0.8333333333x. Take half its coefficient (-0.4166666667). Square it (0.1736111111) and add it to both sides. Add '0.1736111111' to each side of the equation. -0.8333333333x + 0.1736111111 + x2 = 33.33333333 + 0.1736111111 Reorder the terms: 0.1736111111 + -0.8333333333x + x2 = 33.33333333 + 0.1736111111 Combine like terms: 33.33333333 + 0.1736111111 = 33.5069444411 0.1736111111 + -0.8333333333x + x2 = 33.5069444411 Factor a perfect square on the left side: (x + -0.4166666667)(x + -0.4166666667) = 33.5069444411 Calculate the square root of the right side: 5.788518329 Break this problem into two subproblems by setting (x + -0.4166666667) equal to 5.788518329 and -5.788518329.Subproblem 1
x + -0.4166666667 = 5.788518329 Simplifying x + -0.4166666667 = 5.788518329 Reorder the terms: -0.4166666667 + x = 5.788518329 Solving -0.4166666667 + x = 5.788518329 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4166666667' to each side of the equation. -0.4166666667 + 0.4166666667 + x = 5.788518329 + 0.4166666667 Combine like terms: -0.4166666667 + 0.4166666667 = 0.0000000000 0.0000000000 + x = 5.788518329 + 0.4166666667 x = 5.788518329 + 0.4166666667 Combine like terms: 5.788518329 + 0.4166666667 = 6.2051849957 x = 6.2051849957 Simplifying x = 6.2051849957Subproblem 2
x + -0.4166666667 = -5.788518329 Simplifying x + -0.4166666667 = -5.788518329 Reorder the terms: -0.4166666667 + x = -5.788518329 Solving -0.4166666667 + x = -5.788518329 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4166666667' to each side of the equation. -0.4166666667 + 0.4166666667 + x = -5.788518329 + 0.4166666667 Combine like terms: -0.4166666667 + 0.4166666667 = 0.0000000000 0.0000000000 + x = -5.788518329 + 0.4166666667 x = -5.788518329 + 0.4166666667 Combine like terms: -5.788518329 + 0.4166666667 = -5.3718516623 x = -5.3718516623 Simplifying x = -5.3718516623Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.2051849957, -5.3718516623}
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