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Simplifying 18x2 + -43x + 5 = 0 Reorder the terms: 5 + -43x + 18x2 = 0 Solving 5 + -43x + 18x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 18 the coefficient of the squared term: Divide each side by '18'. 0.2777777778 + -2.388888889x + x2 = 0 Move the constant term to the right: Add '-0.2777777778' to each side of the equation. 0.2777777778 + -2.388888889x + -0.2777777778 + x2 = 0 + -0.2777777778 Reorder the terms: 0.2777777778 + -0.2777777778 + -2.388888889x + x2 = 0 + -0.2777777778 Combine like terms: 0.2777777778 + -0.2777777778 = 0.0000000000 0.0000000000 + -2.388888889x + x2 = 0 + -0.2777777778 -2.388888889x + x2 = 0 + -0.2777777778 Combine like terms: 0 + -0.2777777778 = -0.2777777778 -2.388888889x + x2 = -0.2777777778 The x term is -2.388888889x. Take half its coefficient (-1.194444445). Square it (1.426697532) and add it to both sides. Add '1.426697532' to each side of the equation. -2.388888889x + 1.426697532 + x2 = -0.2777777778 + 1.426697532 Reorder the terms: 1.426697532 + -2.388888889x + x2 = -0.2777777778 + 1.426697532 Combine like terms: -0.2777777778 + 1.426697532 = 1.1489197542 1.426697532 + -2.388888889x + x2 = 1.1489197542 Factor a perfect square on the left side: (x + -1.194444445)(x + -1.194444445) = 1.1489197542 Calculate the square root of the right side: 1.071876744 Break this problem into two subproblems by setting (x + -1.194444445) equal to 1.071876744 and -1.071876744.Subproblem 1
x + -1.194444445 = 1.071876744 Simplifying x + -1.194444445 = 1.071876744 Reorder the terms: -1.194444445 + x = 1.071876744 Solving -1.194444445 + x = 1.071876744 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.194444445' to each side of the equation. -1.194444445 + 1.194444445 + x = 1.071876744 + 1.194444445 Combine like terms: -1.194444445 + 1.194444445 = 0.000000000 0.000000000 + x = 1.071876744 + 1.194444445 x = 1.071876744 + 1.194444445 Combine like terms: 1.071876744 + 1.194444445 = 2.266321189 x = 2.266321189 Simplifying x = 2.266321189Subproblem 2
x + -1.194444445 = -1.071876744 Simplifying x + -1.194444445 = -1.071876744 Reorder the terms: -1.194444445 + x = -1.071876744 Solving -1.194444445 + x = -1.071876744 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.194444445' to each side of the equation. -1.194444445 + 1.194444445 + x = -1.071876744 + 1.194444445 Combine like terms: -1.194444445 + 1.194444445 = 0.000000000 0.000000000 + x = -1.071876744 + 1.194444445 x = -1.071876744 + 1.194444445 Combine like terms: -1.071876744 + 1.194444445 = 0.122567701 x = 0.122567701 Simplifying x = 0.122567701Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.266321189, 0.122567701}
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