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Simplifying x2 + 10x = 80 Reorder the terms: 10x + x2 = 80 Solving 10x + x2 = 80 Solving for variable 'x'. Reorder the terms: -80 + 10x + x2 = 80 + -80 Combine like terms: 80 + -80 = 0 -80 + 10x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '80' to each side of the equation. -80 + 10x + 80 + x2 = 0 + 80 Reorder the terms: -80 + 80 + 10x + x2 = 0 + 80 Combine like terms: -80 + 80 = 0 0 + 10x + x2 = 0 + 80 10x + x2 = 0 + 80 Combine like terms: 0 + 80 = 80 10x + x2 = 80 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 = 80 + 25 Reorder the terms: 25 + 10x + x2 = 80 + 25 Combine like terms: 80 + 25 = 105 25 + 10x + x2 = 105 Factor a perfect square on the left side: (x + 5)(x + 5) = 105 Calculate the square root of the right side: 10.246950766 Break this problem into two subproblems by setting (x + 5) equal to 10.246950766 and -10.246950766.Subproblem 1
x + 5 = 10.246950766 Simplifying x + 5 = 10.246950766 Reorder the terms: 5 + x = 10.246950766 Solving 5 + x = 10.246950766 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 = 10.246950766 + -5 Combine like terms: 5 + -5 = 0 0 + x = 10.246950766 + -5 x = 10.246950766 + -5 Combine like terms: 10.246950766 + -5 = 5.246950766 x = 5.246950766 Simplifying x = 5.246950766Subproblem 2
x + 5 = -10.246950766 Simplifying x + 5 = -10.246950766 Reorder the terms: 5 + x = -10.246950766 Solving 5 + x = -10.246950766 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 = -10.246950766 + -5 Combine like terms: 5 + -5 = 0 0 + x = -10.246950766 + -5 x = -10.246950766 + -5 Combine like terms: -10.246950766 + -5 = -15.246950766 x = -15.246950766 Simplifying x = -15.246950766Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.246950766, -15.246950766}
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