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Simplifying x2 + 30x + 112 = 0 Reorder the terms: 112 + 30x + x2 = 0 Solving 112 + 30x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-112' to each side of the equation. 112 + 30x + -112 + x2 = 0 + -112 Reorder the terms: 112 + -112 + 30x + x2 = 0 + -112 Combine like terms: 112 + -112 = 0 0 + 30x + x2 = 0 + -112 30x + x2 = 0 + -112 Combine like terms: 0 + -112 = -112 30x + x2 = -112 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 = -112 + 225 Reorder the terms: 225 + 30x + x2 = -112 + 225 Combine like terms: -112 + 225 = 113 225 + 30x + x2 = 113 Factor a perfect square on the left side: (x + 15)(x + 15) = 113 Calculate the square root of the right side: 10.630145813 Break this problem into two subproblems by setting (x + 15) equal to 10.630145813 and -10.630145813.Subproblem 1
x + 15 = 10.630145813 Simplifying x + 15 = 10.630145813 Reorder the terms: 15 + x = 10.630145813 Solving 15 + x = 10.630145813 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 = 10.630145813 + -15 Combine like terms: 15 + -15 = 0 0 + x = 10.630145813 + -15 x = 10.630145813 + -15 Combine like terms: 10.630145813 + -15 = -4.369854187 x = -4.369854187 Simplifying x = -4.369854187Subproblem 2
x + 15 = -10.630145813 Simplifying x + 15 = -10.630145813 Reorder the terms: 15 + x = -10.630145813 Solving 15 + x = -10.630145813 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 = -10.630145813 + -15 Combine like terms: 15 + -15 = 0 0 + x = -10.630145813 + -15 x = -10.630145813 + -15 Combine like terms: -10.630145813 + -15 = -25.630145813 x = -25.630145813 Simplifying x = -25.630145813Solution
The solution to the problem is based on the solutions from the subproblems. x = {-4.369854187, -25.630145813}
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