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Simplifying x2 + 10x + -1444 = 3 Reorder the terms: -1444 + 10x + x2 = 3 Solving -1444 + 10x + x2 = 3 Solving for variable 'x'. Reorder the terms: -1444 + -3 + 10x + x2 = 3 + -3 Combine like terms: -1444 + -3 = -1447 -1447 + 10x + x2 = 3 + -3 Combine like terms: 3 + -3 = 0 -1447 + 10x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '1447' to each side of the equation. -1447 + 10x + 1447 + x2 = 0 + 1447 Reorder the terms: -1447 + 1447 + 10x + x2 = 0 + 1447 Combine like terms: -1447 + 1447 = 0 0 + 10x + x2 = 0 + 1447 10x + x2 = 0 + 1447 Combine like terms: 0 + 1447 = 1447 10x + x2 = 1447 The x term is 10x. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10x + 25 + x2 = 1447 + 25 Reorder the terms: 25 + 10x + x2 = 1447 + 25 Combine like terms: 1447 + 25 = 1472 25 + 10x + x2 = 1472 Factor a perfect square on the left side: (x + 5)(x + 5) = 1472 Calculate the square root of the right side: 38.366652187 Break this problem into two subproblems by setting (x + 5) equal to 38.366652187 and -38.366652187.Subproblem 1
x + 5 = 38.366652187 Simplifying x + 5 = 38.366652187 Reorder the terms: 5 + x = 38.366652187 Solving 5 + x = 38.366652187 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 38.366652187 + -5 Combine like terms: 5 + -5 = 0 0 + x = 38.366652187 + -5 x = 38.366652187 + -5 Combine like terms: 38.366652187 + -5 = 33.366652187 x = 33.366652187 Simplifying x = 33.366652187Subproblem 2
x + 5 = -38.366652187 Simplifying x + 5 = -38.366652187 Reorder the terms: 5 + x = -38.366652187 Solving 5 + x = -38.366652187 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = -38.366652187 + -5 Combine like terms: 5 + -5 = 0 0 + x = -38.366652187 + -5 x = -38.366652187 + -5 Combine like terms: -38.366652187 + -5 = -43.366652187 x = -43.366652187 Simplifying x = -43.366652187Solution
The solution to the problem is based on the solutions from the subproblems. x = {33.366652187, -43.366652187}
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