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Simplifying x2 + 3x + 10 = 180 Reorder the terms: 10 + 3x + x2 = 180 Solving 10 + 3x + x2 = 180 Solving for variable 'x'. Reorder the terms: 10 + -180 + 3x + x2 = 180 + -180 Combine like terms: 10 + -180 = -170 -170 + 3x + x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -170 + 3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '170' to each side of the equation. -170 + 3x + 170 + x2 = 0 + 170 Reorder the terms: -170 + 170 + 3x + x2 = 0 + 170 Combine like terms: -170 + 170 = 0 0 + 3x + x2 = 0 + 170 3x + x2 = 0 + 170 Combine like terms: 0 + 170 = 170 3x + x2 = 170 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = 170 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 170 + 2.25 Combine like terms: 170 + 2.25 = 172.25 2.25 + 3x + x2 = 172.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 172.25 Calculate the square root of the right side: 13.124404748 Break this problem into two subproblems by setting (x + 1.5) equal to 13.124404748 and -13.124404748.Subproblem 1
x + 1.5 = 13.124404748 Simplifying x + 1.5 = 13.124404748 Reorder the terms: 1.5 + x = 13.124404748 Solving 1.5 + x = 13.124404748 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 13.124404748 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 13.124404748 + -1.5 x = 13.124404748 + -1.5 Combine like terms: 13.124404748 + -1.5 = 11.624404748 x = 11.624404748 Simplifying x = 11.624404748Subproblem 2
x + 1.5 = -13.124404748 Simplifying x + 1.5 = -13.124404748 Reorder the terms: 1.5 + x = -13.124404748 Solving 1.5 + x = -13.124404748 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -13.124404748 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -13.124404748 + -1.5 x = -13.124404748 + -1.5 Combine like terms: -13.124404748 + -1.5 = -14.624404748 x = -14.624404748 Simplifying x = -14.624404748Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.624404748, -14.624404748}
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