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Simplifying 18x2 + -45x + -10 = 0 Reorder the terms: -10 + -45x + 18x2 = 0 Solving -10 + -45x + 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'. -0.5555555556 + -2.5x + x2 = 0 Move the constant term to the right: Add '0.5555555556' to each side of the equation. -0.5555555556 + -2.5x + 0.5555555556 + x2 = 0 + 0.5555555556 Reorder the terms: -0.5555555556 + 0.5555555556 + -2.5x + x2 = 0 + 0.5555555556 Combine like terms: -0.5555555556 + 0.5555555556 = 0.0000000000 0.0000000000 + -2.5x + x2 = 0 + 0.5555555556 -2.5x + x2 = 0 + 0.5555555556 Combine like terms: 0 + 0.5555555556 = 0.5555555556 -2.5x + x2 = 0.5555555556 The x term is -2.5x. Take half its coefficient (-1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. -2.5x + 1.5625 + x2 = 0.5555555556 + 1.5625 Reorder the terms: 1.5625 + -2.5x + x2 = 0.5555555556 + 1.5625 Combine like terms: 0.5555555556 + 1.5625 = 2.1180555556 1.5625 + -2.5x + x2 = 2.1180555556 Factor a perfect square on the left side: (x + -1.25)(x + -1.25) = 2.1180555556 Calculate the square root of the right side: 1.4553541 Break this problem into two subproblems by setting (x + -1.25) equal to 1.4553541 and -1.4553541.Subproblem 1
x + -1.25 = 1.4553541 Simplifying x + -1.25 = 1.4553541 Reorder the terms: -1.25 + x = 1.4553541 Solving -1.25 + x = 1.4553541 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = 1.4553541 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = 1.4553541 + 1.25 x = 1.4553541 + 1.25 Combine like terms: 1.4553541 + 1.25 = 2.7053541 x = 2.7053541 Simplifying x = 2.7053541Subproblem 2
x + -1.25 = -1.4553541 Simplifying x + -1.25 = -1.4553541 Reorder the terms: -1.25 + x = -1.4553541 Solving -1.25 + x = -1.4553541 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = -1.4553541 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = -1.4553541 + 1.25 x = -1.4553541 + 1.25 Combine like terms: -1.4553541 + 1.25 = -0.2053541 x = -0.2053541 Simplifying x = -0.2053541Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.7053541, -0.2053541}
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