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Simplifying x2 + -76.4x + 720 = 0 Reorder the terms: 720 + -76.4x + x2 = 0 Solving 720 + -76.4x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-720' to each side of the equation. 720 + -76.4x + -720 + x2 = 0 + -720 Reorder the terms: 720 + -720 + -76.4x + x2 = 0 + -720 Combine like terms: 720 + -720 = 0 0 + -76.4x + x2 = 0 + -720 -76.4x + x2 = 0 + -720 Combine like terms: 0 + -720 = -720 -76.4x + x2 = -720 The x term is -76.4x. Take half its coefficient (-38.2). Square it (1459.24) and add it to both sides. Add '1459.24' to each side of the equation. -76.4x + 1459.24 + x2 = -720 + 1459.24 Reorder the terms: 1459.24 + -76.4x + x2 = -720 + 1459.24 Combine like terms: -720 + 1459.24 = 739.24 1459.24 + -76.4x + x2 = 739.24 Factor a perfect square on the left side: (x + -38.2)(x + -38.2) = 739.24 Calculate the square root of the right side: 27.188968351 Break this problem into two subproblems by setting (x + -38.2) equal to 27.188968351 and -27.188968351.Subproblem 1
x + -38.2 = 27.188968351 Simplifying x + -38.2 = 27.188968351 Reorder the terms: -38.2 + x = 27.188968351 Solving -38.2 + x = 27.188968351 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '38.2' to each side of the equation. -38.2 + 38.2 + x = 27.188968351 + 38.2 Combine like terms: -38.2 + 38.2 = 0.0 0.0 + x = 27.188968351 + 38.2 x = 27.188968351 + 38.2 Combine like terms: 27.188968351 + 38.2 = 65.388968351 x = 65.388968351 Simplifying x = 65.388968351Subproblem 2
x + -38.2 = -27.188968351 Simplifying x + -38.2 = -27.188968351 Reorder the terms: -38.2 + x = -27.188968351 Solving -38.2 + x = -27.188968351 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '38.2' to each side of the equation. -38.2 + 38.2 + x = -27.188968351 + 38.2 Combine like terms: -38.2 + 38.2 = 0.0 0.0 + x = -27.188968351 + 38.2 x = -27.188968351 + 38.2 Combine like terms: -27.188968351 + 38.2 = 11.011031649 x = 11.011031649 Simplifying x = 11.011031649Solution
The solution to the problem is based on the solutions from the subproblems. x = {65.388968351, 11.011031649}
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