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Simplifying x2 + 12x + -460 = 0 Reorder the terms: -460 + 12x + x2 = 0 Solving -460 + 12x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '460' to each side of the equation. -460 + 12x + 460 + x2 = 0 + 460 Reorder the terms: -460 + 460 + 12x + x2 = 0 + 460 Combine like terms: -460 + 460 = 0 0 + 12x + x2 = 0 + 460 12x + x2 = 0 + 460 Combine like terms: 0 + 460 = 460 12x + x2 = 460 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 = 460 + 36 Reorder the terms: 36 + 12x + x2 = 460 + 36 Combine like terms: 460 + 36 = 496 36 + 12x + x2 = 496 Factor a perfect square on the left side: (x + 6)(x + 6) = 496 Calculate the square root of the right side: 22.271057451 Break this problem into two subproblems by setting (x + 6) equal to 22.271057451 and -22.271057451.Subproblem 1
x + 6 = 22.271057451 Simplifying x + 6 = 22.271057451 Reorder the terms: 6 + x = 22.271057451 Solving 6 + x = 22.271057451 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 = 22.271057451 + -6 Combine like terms: 6 + -6 = 0 0 + x = 22.271057451 + -6 x = 22.271057451 + -6 Combine like terms: 22.271057451 + -6 = 16.271057451 x = 16.271057451 Simplifying x = 16.271057451Subproblem 2
x + 6 = -22.271057451 Simplifying x + 6 = -22.271057451 Reorder the terms: 6 + x = -22.271057451 Solving 6 + x = -22.271057451 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 = -22.271057451 + -6 Combine like terms: 6 + -6 = 0 0 + x = -22.271057451 + -6 x = -22.271057451 + -6 Combine like terms: -22.271057451 + -6 = -28.271057451 x = -28.271057451 Simplifying x = -28.271057451Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.271057451, -28.271057451}
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