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Simplifying x2 + -39x + 72.3 = 0 Reorder the terms: 72.3 + -39x + x2 = 0 Solving 72.3 + -39x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-72.3' to each side of the equation. 72.3 + -39x + -72.3 + x2 = 0 + -72.3 Reorder the terms: 72.3 + -72.3 + -39x + x2 = 0 + -72.3 Combine like terms: 72.3 + -72.3 = 0.0 0.0 + -39x + x2 = 0 + -72.3 -39x + x2 = 0 + -72.3 Combine like terms: 0 + -72.3 = -72.3 -39x + x2 = -72.3 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 = -72.3 + 380.25 Reorder the terms: 380.25 + -39x + x2 = -72.3 + 380.25 Combine like terms: -72.3 + 380.25 = 307.95 380.25 + -39x + x2 = 307.95 Factor a perfect square on the left side: (x + -19.5)(x + -19.5) = 307.95 Calculate the square root of the right side: 17.54850421 Break this problem into two subproblems by setting (x + -19.5) equal to 17.54850421 and -17.54850421.Subproblem 1
x + -19.5 = 17.54850421 Simplifying x + -19.5 = 17.54850421 Reorder the terms: -19.5 + x = 17.54850421 Solving -19.5 + x = 17.54850421 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 = 17.54850421 + 19.5 Combine like terms: -19.5 + 19.5 = 0.0 0.0 + x = 17.54850421 + 19.5 x = 17.54850421 + 19.5 Combine like terms: 17.54850421 + 19.5 = 37.04850421 x = 37.04850421 Simplifying x = 37.04850421Subproblem 2
x + -19.5 = -17.54850421 Simplifying x + -19.5 = -17.54850421 Reorder the terms: -19.5 + x = -17.54850421 Solving -19.5 + x = -17.54850421 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 = -17.54850421 + 19.5 Combine like terms: -19.5 + 19.5 = 0.0 0.0 + x = -17.54850421 + 19.5 x = -17.54850421 + 19.5 Combine like terms: -17.54850421 + 19.5 = 1.95149579 x = 1.95149579 Simplifying x = 1.95149579Solution
The solution to the problem is based on the solutions from the subproblems. x = {37.04850421, 1.95149579}
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