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Simplifying x2 + -34.64x = 13 Reorder the terms: -34.64x + x2 = 13 Solving -34.64x + x2 = 13 Solving for variable 'x'. Reorder the terms: -13 + -34.64x + x2 = 13 + -13 Combine like terms: 13 + -13 = 0 -13 + -34.64x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '13' to each side of the equation. -13 + -34.64x + 13 + x2 = 0 + 13 Reorder the terms: -13 + 13 + -34.64x + x2 = 0 + 13 Combine like terms: -13 + 13 = 0 0 + -34.64x + x2 = 0 + 13 -34.64x + x2 = 0 + 13 Combine like terms: 0 + 13 = 13 -34.64x + x2 = 13 The x term is -34.64x. Take half its coefficient (-17.32). Square it (299.9824) and add it to both sides. Add '299.9824' to each side of the equation. -34.64x + 299.9824 + x2 = 13 + 299.9824 Reorder the terms: 299.9824 + -34.64x + x2 = 13 + 299.9824 Combine like terms: 13 + 299.9824 = 312.9824 299.9824 + -34.64x + x2 = 312.9824 Factor a perfect square on the left side: (x + -17.32)(x + -17.32) = 312.9824 Calculate the square root of the right side: 17.691308601 Break this problem into two subproblems by setting (x + -17.32) equal to 17.691308601 and -17.691308601.Subproblem 1
x + -17.32 = 17.691308601 Simplifying x + -17.32 = 17.691308601 Reorder the terms: -17.32 + x = 17.691308601 Solving -17.32 + x = 17.691308601 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '17.32' to each side of the equation. -17.32 + 17.32 + x = 17.691308601 + 17.32 Combine like terms: -17.32 + 17.32 = 0.00 0.00 + x = 17.691308601 + 17.32 x = 17.691308601 + 17.32 Combine like terms: 17.691308601 + 17.32 = 35.011308601 x = 35.011308601 Simplifying x = 35.011308601Subproblem 2
x + -17.32 = -17.691308601 Simplifying x + -17.32 = -17.691308601 Reorder the terms: -17.32 + x = -17.691308601 Solving -17.32 + x = -17.691308601 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '17.32' to each side of the equation. -17.32 + 17.32 + x = -17.691308601 + 17.32 Combine like terms: -17.32 + 17.32 = 0.00 0.00 + x = -17.691308601 + 17.32 x = -17.691308601 + 17.32 Combine like terms: -17.691308601 + 17.32 = -0.371308601 x = -0.371308601 Simplifying x = -0.371308601Solution
The solution to the problem is based on the solutions from the subproblems. x = {35.011308601, -0.371308601}
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