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Simplifying x2 + 30x + 162 = 0 Reorder the terms: 162 + 30x + x2 = 0 Solving 162 + 30x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-162' to each side of the equation. 162 + 30x + -162 + x2 = 0 + -162 Reorder the terms: 162 + -162 + 30x + x2 = 0 + -162 Combine like terms: 162 + -162 = 0 0 + 30x + x2 = 0 + -162 30x + x2 = 0 + -162 Combine like terms: 0 + -162 = -162 30x + x2 = -162 The x term is 30x. Take half its coefficient (15). Square it (225) and add it to both sides. Add '225' to each side of the equation. 30x + 225 + x2 = -162 + 225 Reorder the terms: 225 + 30x + x2 = -162 + 225 Combine like terms: -162 + 225 = 63 225 + 30x + x2 = 63 Factor a perfect square on the left side: (x + 15)(x + 15) = 63 Calculate the square root of the right side: 7.937253933 Break this problem into two subproblems by setting (x + 15) equal to 7.937253933 and -7.937253933.Subproblem 1
x + 15 = 7.937253933 Simplifying x + 15 = 7.937253933 Reorder the terms: 15 + x = 7.937253933 Solving 15 + x = 7.937253933 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + x = 7.937253933 + -15 Combine like terms: 15 + -15 = 0 0 + x = 7.937253933 + -15 x = 7.937253933 + -15 Combine like terms: 7.937253933 + -15 = -7.062746067 x = -7.062746067 Simplifying x = -7.062746067Subproblem 2
x + 15 = -7.937253933 Simplifying x + 15 = -7.937253933 Reorder the terms: 15 + x = -7.937253933 Solving 15 + x = -7.937253933 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + x = -7.937253933 + -15 Combine like terms: 15 + -15 = 0 0 + x = -7.937253933 + -15 x = -7.937253933 + -15 Combine like terms: -7.937253933 + -15 = -22.937253933 x = -22.937253933 Simplifying x = -22.937253933Solution
The solution to the problem is based on the solutions from the subproblems. x = {-7.062746067, -22.937253933}
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