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Simplifying x2 + 12x + -175 = 0 Reorder the terms: -175 + 12x + x2 = 0 Solving -175 + 12x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '175' to each side of the equation. -175 + 12x + 175 + x2 = 0 + 175 Reorder the terms: -175 + 175 + 12x + x2 = 0 + 175 Combine like terms: -175 + 175 = 0 0 + 12x + x2 = 0 + 175 12x + x2 = 0 + 175 Combine like terms: 0 + 175 = 175 12x + x2 = 175 The x term is 12x. Take half its coefficient (6). Square it (36) and add it to both sides. Add '36' to each side of the equation. 12x + 36 + x2 = 175 + 36 Reorder the terms: 36 + 12x + x2 = 175 + 36 Combine like terms: 175 + 36 = 211 36 + 12x + x2 = 211 Factor a perfect square on the left side: (x + 6)(x + 6) = 211 Calculate the square root of the right side: 14.525839046 Break this problem into two subproblems by setting (x + 6) equal to 14.525839046 and -14.525839046.Subproblem 1
x + 6 = 14.525839046 Simplifying x + 6 = 14.525839046 Reorder the terms: 6 + x = 14.525839046 Solving 6 + x = 14.525839046 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = 14.525839046 + -6 Combine like terms: 6 + -6 = 0 0 + x = 14.525839046 + -6 x = 14.525839046 + -6 Combine like terms: 14.525839046 + -6 = 8.525839046 x = 8.525839046 Simplifying x = 8.525839046Subproblem 2
x + 6 = -14.525839046 Simplifying x + 6 = -14.525839046 Reorder the terms: 6 + x = -14.525839046 Solving 6 + x = -14.525839046 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = -14.525839046 + -6 Combine like terms: 6 + -6 = 0 0 + x = -14.525839046 + -6 x = -14.525839046 + -6 Combine like terms: -14.525839046 + -6 = -20.525839046 x = -20.525839046 Simplifying x = -20.525839046Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.525839046, -20.525839046}
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