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Simplifying x2 + 10x = 30 Reorder the terms: 10x + x2 = 30 Solving 10x + x2 = 30 Solving for variable 'x'. Reorder the terms: -30 + 10x + x2 = 30 + -30 Combine like terms: 30 + -30 = 0 -30 + 10x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '30' to each side of the equation. -30 + 10x + 30 + x2 = 0 + 30 Reorder the terms: -30 + 30 + 10x + x2 = 0 + 30 Combine like terms: -30 + 30 = 0 0 + 10x + x2 = 0 + 30 10x + x2 = 0 + 30 Combine like terms: 0 + 30 = 30 10x + x2 = 30 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 = 30 + 25 Reorder the terms: 25 + 10x + x2 = 30 + 25 Combine like terms: 30 + 25 = 55 25 + 10x + x2 = 55 Factor a perfect square on the left side: (x + 5)(x + 5) = 55 Calculate the square root of the right side: 7.416198487 Break this problem into two subproblems by setting (x + 5) equal to 7.416198487 and -7.416198487.Subproblem 1
x + 5 = 7.416198487 Simplifying x + 5 = 7.416198487 Reorder the terms: 5 + x = 7.416198487 Solving 5 + x = 7.416198487 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 = 7.416198487 + -5 Combine like terms: 5 + -5 = 0 0 + x = 7.416198487 + -5 x = 7.416198487 + -5 Combine like terms: 7.416198487 + -5 = 2.416198487 x = 2.416198487 Simplifying x = 2.416198487Subproblem 2
x + 5 = -7.416198487 Simplifying x + 5 = -7.416198487 Reorder the terms: 5 + x = -7.416198487 Solving 5 + x = -7.416198487 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 = -7.416198487 + -5 Combine like terms: 5 + -5 = 0 0 + x = -7.416198487 + -5 x = -7.416198487 + -5 Combine like terms: -7.416198487 + -5 = -12.416198487 x = -12.416198487 Simplifying x = -12.416198487Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.416198487, -12.416198487}
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