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Simplifying x2 + -84x + 396 = 0 Reorder the terms: 396 + -84x + x2 = 0 Solving 396 + -84x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-396' to each side of the equation. 396 + -84x + -396 + x2 = 0 + -396 Reorder the terms: 396 + -396 + -84x + x2 = 0 + -396 Combine like terms: 396 + -396 = 0 0 + -84x + x2 = 0 + -396 -84x + x2 = 0 + -396 Combine like terms: 0 + -396 = -396 -84x + x2 = -396 The x term is -84x. Take half its coefficient (-42). Square it (1764) and add it to both sides. Add '1764' to each side of the equation. -84x + 1764 + x2 = -396 + 1764 Reorder the terms: 1764 + -84x + x2 = -396 + 1764 Combine like terms: -396 + 1764 = 1368 1764 + -84x + x2 = 1368 Factor a perfect square on the left side: (x + -42)(x + -42) = 1368 Calculate the square root of the right side: 36.986484018 Break this problem into two subproblems by setting (x + -42) equal to 36.986484018 and -36.986484018.Subproblem 1
x + -42 = 36.986484018 Simplifying x + -42 = 36.986484018 Reorder the terms: -42 + x = 36.986484018 Solving -42 + x = 36.986484018 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '42' to each side of the equation. -42 + 42 + x = 36.986484018 + 42 Combine like terms: -42 + 42 = 0 0 + x = 36.986484018 + 42 x = 36.986484018 + 42 Combine like terms: 36.986484018 + 42 = 78.986484018 x = 78.986484018 Simplifying x = 78.986484018Subproblem 2
x + -42 = -36.986484018 Simplifying x + -42 = -36.986484018 Reorder the terms: -42 + x = -36.986484018 Solving -42 + x = -36.986484018 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '42' to each side of the equation. -42 + 42 + x = -36.986484018 + 42 Combine like terms: -42 + 42 = 0 0 + x = -36.986484018 + 42 x = -36.986484018 + 42 Combine like terms: -36.986484018 + 42 = 5.013515982 x = 5.013515982 Simplifying x = 5.013515982Solution
The solution to the problem is based on the solutions from the subproblems. x = {78.986484018, 5.013515982}
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