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Simplifying 13.2x + x2 + -1296 = 0 Reorder the terms: -1296 + 13.2x + x2 = 0 Solving -1296 + 13.2x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '1296' to each side of the equation. -1296 + 13.2x + 1296 + x2 = 0 + 1296 Reorder the terms: -1296 + 1296 + 13.2x + x2 = 0 + 1296 Combine like terms: -1296 + 1296 = 0 0 + 13.2x + x2 = 0 + 1296 13.2x + x2 = 0 + 1296 Combine like terms: 0 + 1296 = 1296 13.2x + x2 = 1296 The x term is 13.2x. Take half its coefficient (6.6). Square it (43.56) and add it to both sides. Add '43.56' to each side of the equation. 13.2x + 43.56 + x2 = 1296 + 43.56 Reorder the terms: 43.56 + 13.2x + x2 = 1296 + 43.56 Combine like terms: 1296 + 43.56 = 1339.56 43.56 + 13.2x + x2 = 1339.56 Factor a perfect square on the left side: (x + 6.6)(x + 6.6) = 1339.56 Calculate the square root of the right side: 36.6 Break this problem into two subproblems by setting (x + 6.6) equal to 36.6 and -36.6.Subproblem 1
x + 6.6 = 36.6 Simplifying x + 6.6 = 36.6 Reorder the terms: 6.6 + x = 36.6 Solving 6.6 + x = 36.6 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.6' to each side of the equation. 6.6 + -6.6 + x = 36.6 + -6.6 Combine like terms: 6.6 + -6.6 = 0.0 0.0 + x = 36.6 + -6.6 x = 36.6 + -6.6 Combine like terms: 36.6 + -6.6 = 30 x = 30 Simplifying x = 30Subproblem 2
x + 6.6 = -36.6 Simplifying x + 6.6 = -36.6 Reorder the terms: 6.6 + x = -36.6 Solving 6.6 + x = -36.6 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.6' to each side of the equation. 6.6 + -6.6 + x = -36.6 + -6.6 Combine like terms: 6.6 + -6.6 = 0.0 0.0 + x = -36.6 + -6.6 x = -36.6 + -6.6 Combine like terms: -36.6 + -6.6 = -43.2 x = -43.2 Simplifying x = -43.2Solution
The solution to the problem is based on the solutions from the subproblems. x = {30, -43.2}
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