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Simplifying x2 + -42x + -216 = 0 Reorder the terms: -216 + -42x + x2 = 0 Solving -216 + -42x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '216' to each side of the equation. -216 + -42x + 216 + x2 = 0 + 216 Reorder the terms: -216 + 216 + -42x + x2 = 0 + 216 Combine like terms: -216 + 216 = 0 0 + -42x + x2 = 0 + 216 -42x + x2 = 0 + 216 Combine like terms: 0 + 216 = 216 -42x + x2 = 216 The x term is -42x. Take half its coefficient (-21). Square it (441) and add it to both sides. Add '441' to each side of the equation. -42x + 441 + x2 = 216 + 441 Reorder the terms: 441 + -42x + x2 = 216 + 441 Combine like terms: 216 + 441 = 657 441 + -42x + x2 = 657 Factor a perfect square on the left side: (x + -21)(x + -21) = 657 Calculate the square root of the right side: 25.632011236 Break this problem into two subproblems by setting (x + -21) equal to 25.632011236 and -25.632011236.Subproblem 1
x + -21 = 25.632011236 Simplifying x + -21 = 25.632011236 Reorder the terms: -21 + x = 25.632011236 Solving -21 + x = 25.632011236 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '21' to each side of the equation. -21 + 21 + x = 25.632011236 + 21 Combine like terms: -21 + 21 = 0 0 + x = 25.632011236 + 21 x = 25.632011236 + 21 Combine like terms: 25.632011236 + 21 = 46.632011236 x = 46.632011236 Simplifying x = 46.632011236Subproblem 2
x + -21 = -25.632011236 Simplifying x + -21 = -25.632011236 Reorder the terms: -21 + x = -25.632011236 Solving -21 + x = -25.632011236 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '21' to each side of the equation. -21 + 21 + x = -25.632011236 + 21 Combine like terms: -21 + 21 = 0 0 + x = -25.632011236 + 21 x = -25.632011236 + 21 Combine like terms: -25.632011236 + 21 = -4.632011236 x = -4.632011236 Simplifying x = -4.632011236Solution
The solution to the problem is based on the solutions from the subproblems. x = {46.632011236, -4.632011236}
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