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Simplifying 13.2x + x2 + -1246 = 0 Reorder the terms: -1246 + 13.2x + x2 = 0 Solving -1246 + 13.2x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '1246' to each side of the equation. -1246 + 13.2x + 1246 + x2 = 0 + 1246 Reorder the terms: -1246 + 1246 + 13.2x + x2 = 0 + 1246 Combine like terms: -1246 + 1246 = 0 0 + 13.2x + x2 = 0 + 1246 13.2x + x2 = 0 + 1246 Combine like terms: 0 + 1246 = 1246 13.2x + x2 = 1246 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 = 1246 + 43.56 Reorder the terms: 43.56 + 13.2x + x2 = 1246 + 43.56 Combine like terms: 1246 + 43.56 = 1289.56 43.56 + 13.2x + x2 = 1289.56 Factor a perfect square on the left side: (x + 6.6)(x + 6.6) = 1289.56 Calculate the square root of the right side: 35.910444163 Break this problem into two subproblems by setting (x + 6.6) equal to 35.910444163 and -35.910444163.Subproblem 1
x + 6.6 = 35.910444163 Simplifying x + 6.6 = 35.910444163 Reorder the terms: 6.6 + x = 35.910444163 Solving 6.6 + x = 35.910444163 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 = 35.910444163 + -6.6 Combine like terms: 6.6 + -6.6 = 0.0 0.0 + x = 35.910444163 + -6.6 x = 35.910444163 + -6.6 Combine like terms: 35.910444163 + -6.6 = 29.310444163 x = 29.310444163 Simplifying x = 29.310444163Subproblem 2
x + 6.6 = -35.910444163 Simplifying x + 6.6 = -35.910444163 Reorder the terms: 6.6 + x = -35.910444163 Solving 6.6 + x = -35.910444163 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 = -35.910444163 + -6.6 Combine like terms: 6.6 + -6.6 = 0.0 0.0 + x = -35.910444163 + -6.6 x = -35.910444163 + -6.6 Combine like terms: -35.910444163 + -6.6 = -42.510444163 x = -42.510444163 Simplifying x = -42.510444163Solution
The solution to the problem is based on the solutions from the subproblems. x = {29.310444163, -42.510444163}
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