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Simplifying x2 + 10x + -74 = 0 Reorder the terms: -74 + 10x + x2 = 0 Solving -74 + 10x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '74' to each side of the equation. -74 + 10x + 74 + x2 = 0 + 74 Reorder the terms: -74 + 74 + 10x + x2 = 0 + 74 Combine like terms: -74 + 74 = 0 0 + 10x + x2 = 0 + 74 10x + x2 = 0 + 74 Combine like terms: 0 + 74 = 74 10x + x2 = 74 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 = 74 + 25 Reorder the terms: 25 + 10x + x2 = 74 + 25 Combine like terms: 74 + 25 = 99 25 + 10x + x2 = 99 Factor a perfect square on the left side: (x + 5)(x + 5) = 99 Calculate the square root of the right side: 9.949874371 Break this problem into two subproblems by setting (x + 5) equal to 9.949874371 and -9.949874371.Subproblem 1
x + 5 = 9.949874371 Simplifying x + 5 = 9.949874371 Reorder the terms: 5 + x = 9.949874371 Solving 5 + x = 9.949874371 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 = 9.949874371 + -5 Combine like terms: 5 + -5 = 0 0 + x = 9.949874371 + -5 x = 9.949874371 + -5 Combine like terms: 9.949874371 + -5 = 4.949874371 x = 4.949874371 Simplifying x = 4.949874371Subproblem 2
x + 5 = -9.949874371 Simplifying x + 5 = -9.949874371 Reorder the terms: 5 + x = -9.949874371 Solving 5 + x = -9.949874371 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 = -9.949874371 + -5 Combine like terms: 5 + -5 = 0 0 + x = -9.949874371 + -5 x = -9.949874371 + -5 Combine like terms: -9.949874371 + -5 = -14.949874371 x = -14.949874371 Simplifying x = -14.949874371Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.949874371, -14.949874371}
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