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Simplifying x2 + 32x + 45 = 0 Reorder the terms: 45 + 32x + x2 = 0 Solving 45 + 32x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-45' to each side of the equation. 45 + 32x + -45 + x2 = 0 + -45 Reorder the terms: 45 + -45 + 32x + x2 = 0 + -45 Combine like terms: 45 + -45 = 0 0 + 32x + x2 = 0 + -45 32x + x2 = 0 + -45 Combine like terms: 0 + -45 = -45 32x + x2 = -45 The x term is 32x. Take half its coefficient (16). Square it (256) and add it to both sides. Add '256' to each side of the equation. 32x + 256 + x2 = -45 + 256 Reorder the terms: 256 + 32x + x2 = -45 + 256 Combine like terms: -45 + 256 = 211 256 + 32x + x2 = 211 Factor a perfect square on the left side: (x + 16)(x + 16) = 211 Calculate the square root of the right side: 14.525839046 Break this problem into two subproblems by setting (x + 16) equal to 14.525839046 and -14.525839046.Subproblem 1
x + 16 = 14.525839046 Simplifying x + 16 = 14.525839046 Reorder the terms: 16 + x = 14.525839046 Solving 16 + x = 14.525839046 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-16' to each side of the equation. 16 + -16 + x = 14.525839046 + -16 Combine like terms: 16 + -16 = 0 0 + x = 14.525839046 + -16 x = 14.525839046 + -16 Combine like terms: 14.525839046 + -16 = -1.474160954 x = -1.474160954 Simplifying x = -1.474160954Subproblem 2
x + 16 = -14.525839046 Simplifying x + 16 = -14.525839046 Reorder the terms: 16 + x = -14.525839046 Solving 16 + x = -14.525839046 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-16' to each side of the equation. 16 + -16 + x = -14.525839046 + -16 Combine like terms: 16 + -16 = 0 0 + x = -14.525839046 + -16 x = -14.525839046 + -16 Combine like terms: -14.525839046 + -16 = -30.525839046 x = -30.525839046 Simplifying x = -30.525839046Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.474160954, -30.525839046}
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