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Simplifying (x * x) + (x * 2) = 3364 Multiply x * x (x2) + (x * 2) = 3364 x2 + (x * 2) = 3364 Reorder the terms for easier multiplication: x2 + (2x) = 3364 Reorder the terms: (2x) + x2 = 3364 Solving (2x) + x2 = 3364 Solving for variable 'x'. Reorder the terms: -3364 + (2x) + x2 = 3364 + -3364 Combine like terms: 3364 + -3364 = 0 -3364 + (2x) + x2 = 0 Begin completing the square. Move the constant term to the right: Add '3364' to each side of the equation. -3364 + (2x) + 3364 + x2 = 0 + 3364 Reorder the terms: -3364 + 3364 + (2x) + x2 = 0 + 3364 Combine like terms: -3364 + 3364 = 0 0 + (2x) + x2 = 0 + 3364 (2x) + x2 = 0 + 3364 Combine like terms: 0 + 3364 = 3364 (2x) + x2 = 3364 The x term is (2x). Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. (2x) + 1 + x2 = 3364 + 1 Reorder the terms: 1 + (2x) + x2 = 3364 + 1 Combine like terms: 3364 + 1 = 3365 1 + (2x) + x2 = 3365 Factor a perfect square on the left side: (x + 1)(x + 1) = 3365 Calculate the square root of the right side: 58.008620049 Break this problem into two subproblems by setting (x + 1) equal to 58.008620049 and -58.008620049.Subproblem 1
x + 1 = 58.008620049 Simplifying x + 1 = 58.008620049 Reorder the terms: 1 + x = 58.008620049 Solving 1 + x = 58.008620049 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 58.008620049 + -1 Combine like terms: 1 + -1 = 0 0 + x = 58.008620049 + -1 x = 58.008620049 + -1 Combine like terms: 58.008620049 + -1 = 57.008620049 x = 57.008620049 Simplifying x = 57.008620049Subproblem 2
x + 1 = -58.008620049 Simplifying x + 1 = -58.008620049 Reorder the terms: 1 + x = -58.008620049 Solving 1 + x = -58.008620049 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -58.008620049 + -1 Combine like terms: 1 + -1 = 0 0 + x = -58.008620049 + -1 x = -58.008620049 + -1 Combine like terms: -58.008620049 + -1 = -59.008620049 x = -59.008620049 Simplifying x = -59.008620049Solution
The solution to the problem is based on the solutions from the subproblems. x = {57.008620049, -59.008620049}
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