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Simplifying 5x2 + -18x + 10 = 0 Reorder the terms: 10 + -18x + 5x2 = 0 Solving 10 + -18x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 2 + -3.6x + x2 = 0 Move the constant term to the right: Add '-2' to each side of the equation. 2 + -3.6x + -2 + x2 = 0 + -2 Reorder the terms: 2 + -2 + -3.6x + x2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -3.6x + x2 = 0 + -2 -3.6x + x2 = 0 + -2 Combine like terms: 0 + -2 = -2 -3.6x + x2 = -2 The x term is -3.6x. Take half its coefficient (-1.8). Square it (3.24) and add it to both sides. Add '3.24' to each side of the equation. -3.6x + 3.24 + x2 = -2 + 3.24 Reorder the terms: 3.24 + -3.6x + x2 = -2 + 3.24 Combine like terms: -2 + 3.24 = 1.24 3.24 + -3.6x + x2 = 1.24 Factor a perfect square on the left side: (x + -1.8)(x + -1.8) = 1.24 Calculate the square root of the right side: 1.113552873 Break this problem into two subproblems by setting (x + -1.8) equal to 1.113552873 and -1.113552873.Subproblem 1
x + -1.8 = 1.113552873 Simplifying x + -1.8 = 1.113552873 Reorder the terms: -1.8 + x = 1.113552873 Solving -1.8 + x = 1.113552873 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.8' to each side of the equation. -1.8 + 1.8 + x = 1.113552873 + 1.8 Combine like terms: -1.8 + 1.8 = 0.0 0.0 + x = 1.113552873 + 1.8 x = 1.113552873 + 1.8 Combine like terms: 1.113552873 + 1.8 = 2.913552873 x = 2.913552873 Simplifying x = 2.913552873Subproblem 2
x + -1.8 = -1.113552873 Simplifying x + -1.8 = -1.113552873 Reorder the terms: -1.8 + x = -1.113552873 Solving -1.8 + x = -1.113552873 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.8' to each side of the equation. -1.8 + 1.8 + x = -1.113552873 + 1.8 Combine like terms: -1.8 + 1.8 = 0.0 0.0 + x = -1.113552873 + 1.8 x = -1.113552873 + 1.8 Combine like terms: -1.113552873 + 1.8 = 0.686447127 x = 0.686447127 Simplifying x = 0.686447127Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.913552873, 0.686447127}
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