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Simplifying x2 + -39x + -5.40 = 0 Reorder the terms: -5.40 + -39x + x2 = 0 Solving -5.40 + -39x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '5.40' to each side of the equation. -5.40 + -39x + 5.40 + x2 = 0 + 5.40 Reorder the terms: -5.40 + 5.40 + -39x + x2 = 0 + 5.40 Combine like terms: -5.40 + 5.40 = 0.00 0.00 + -39x + x2 = 0 + 5.40 -39x + x2 = 0 + 5.40 Combine like terms: 0 + 5.40 = 5.4 -39x + x2 = 5.4 The x term is -39x. Take half its coefficient (-19.5). Square it (380.25) and add it to both sides. Add '380.25' to each side of the equation. -39x + 380.25 + x2 = 5.4 + 380.25 Reorder the terms: 380.25 + -39x + x2 = 5.4 + 380.25 Combine like terms: 5.4 + 380.25 = 385.65 380.25 + -39x + x2 = 385.65 Factor a perfect square on the left side: (x + -19.5)(x + -19.5) = 385.65 Calculate the square root of the right side: 19.637973419 Break this problem into two subproblems by setting (x + -19.5) equal to 19.637973419 and -19.637973419.Subproblem 1
x + -19.5 = 19.637973419 Simplifying x + -19.5 = 19.637973419 Reorder the terms: -19.5 + x = 19.637973419 Solving -19.5 + x = 19.637973419 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '19.5' to each side of the equation. -19.5 + 19.5 + x = 19.637973419 + 19.5 Combine like terms: -19.5 + 19.5 = 0.0 0.0 + x = 19.637973419 + 19.5 x = 19.637973419 + 19.5 Combine like terms: 19.637973419 + 19.5 = 39.137973419 x = 39.137973419 Simplifying x = 39.137973419Subproblem 2
x + -19.5 = -19.637973419 Simplifying x + -19.5 = -19.637973419 Reorder the terms: -19.5 + x = -19.637973419 Solving -19.5 + x = -19.637973419 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '19.5' to each side of the equation. -19.5 + 19.5 + x = -19.637973419 + 19.5 Combine like terms: -19.5 + 19.5 = 0.0 0.0 + x = -19.637973419 + 19.5 x = -19.637973419 + 19.5 Combine like terms: -19.637973419 + 19.5 = -0.137973419 x = -0.137973419 Simplifying x = -0.137973419Solution
The solution to the problem is based on the solutions from the subproblems. x = {39.137973419, -0.137973419}
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