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Simplifying 18x2 + 16x + -3 = 0 Reorder the terms: -3 + 16x + 18x2 = 0 Solving -3 + 16x + 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'. -0.1666666667 + 0.8888888889x + x2 = 0 Move the constant term to the right: Add '0.1666666667' to each side of the equation. -0.1666666667 + 0.8888888889x + 0.1666666667 + x2 = 0 + 0.1666666667 Reorder the terms: -0.1666666667 + 0.1666666667 + 0.8888888889x + x2 = 0 + 0.1666666667 Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000 0.0000000000 + 0.8888888889x + x2 = 0 + 0.1666666667 0.8888888889x + x2 = 0 + 0.1666666667 Combine like terms: 0 + 0.1666666667 = 0.1666666667 0.8888888889x + x2 = 0.1666666667 The x term is 0.8888888889x. Take half its coefficient (0.4444444445). Square it (0.1975308642) and add it to both sides. Add '0.1975308642' to each side of the equation. 0.8888888889x + 0.1975308642 + x2 = 0.1666666667 + 0.1975308642 Reorder the terms: 0.1975308642 + 0.8888888889x + x2 = 0.1666666667 + 0.1975308642 Combine like terms: 0.1666666667 + 0.1975308642 = 0.3641975309 0.1975308642 + 0.8888888889x + x2 = 0.3641975309 Factor a perfect square on the left side: (x + 0.4444444445)(x + 0.4444444445) = 0.3641975309 Calculate the square root of the right side: 0.603487805 Break this problem into two subproblems by setting (x + 0.4444444445) equal to 0.603487805 and -0.603487805.Subproblem 1
x + 0.4444444445 = 0.603487805 Simplifying x + 0.4444444445 = 0.603487805 Reorder the terms: 0.4444444445 + x = 0.603487805 Solving 0.4444444445 + x = 0.603487805 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4444444445' to each side of the equation. 0.4444444445 + -0.4444444445 + x = 0.603487805 + -0.4444444445 Combine like terms: 0.4444444445 + -0.4444444445 = 0.0000000000 0.0000000000 + x = 0.603487805 + -0.4444444445 x = 0.603487805 + -0.4444444445 Combine like terms: 0.603487805 + -0.4444444445 = 0.1590433605 x = 0.1590433605 Simplifying x = 0.1590433605Subproblem 2
x + 0.4444444445 = -0.603487805 Simplifying x + 0.4444444445 = -0.603487805 Reorder the terms: 0.4444444445 + x = -0.603487805 Solving 0.4444444445 + x = -0.603487805 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4444444445' to each side of the equation. 0.4444444445 + -0.4444444445 + x = -0.603487805 + -0.4444444445 Combine like terms: 0.4444444445 + -0.4444444445 = 0.0000000000 0.0000000000 + x = -0.603487805 + -0.4444444445 x = -0.603487805 + -0.4444444445 Combine like terms: -0.603487805 + -0.4444444445 = -1.0479322495 x = -1.0479322495 Simplifying x = -1.0479322495Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.1590433605, -1.0479322495}
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