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Simplifying 10x + x2 = 84 Solving 10x + x2 = 84 Solving for variable 'x'. Reorder the terms: -84 + 10x + x2 = 84 + -84 Combine like terms: 84 + -84 = 0 -84 + 10x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '84' to each side of the equation. -84 + 10x + 84 + x2 = 0 + 84 Reorder the terms: -84 + 84 + 10x + x2 = 0 + 84 Combine like terms: -84 + 84 = 0 0 + 10x + x2 = 0 + 84 10x + x2 = 0 + 84 Combine like terms: 0 + 84 = 84 10x + x2 = 84 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 = 84 + 25 Reorder the terms: 25 + 10x + x2 = 84 + 25 Combine like terms: 84 + 25 = 109 25 + 10x + x2 = 109 Factor a perfect square on the left side: (x + 5)(x + 5) = 109 Calculate the square root of the right side: 10.440306509 Break this problem into two subproblems by setting (x + 5) equal to 10.440306509 and -10.440306509.Subproblem 1
x + 5 = 10.440306509 Simplifying x + 5 = 10.440306509 Reorder the terms: 5 + x = 10.440306509 Solving 5 + x = 10.440306509 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 = 10.440306509 + -5 Combine like terms: 5 + -5 = 0 0 + x = 10.440306509 + -5 x = 10.440306509 + -5 Combine like terms: 10.440306509 + -5 = 5.440306509 x = 5.440306509 Simplifying x = 5.440306509Subproblem 2
x + 5 = -10.440306509 Simplifying x + 5 = -10.440306509 Reorder the terms: 5 + x = -10.440306509 Solving 5 + x = -10.440306509 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 = -10.440306509 + -5 Combine like terms: 5 + -5 = 0 0 + x = -10.440306509 + -5 x = -10.440306509 + -5 Combine like terms: -10.440306509 + -5 = -15.440306509 x = -15.440306509 Simplifying x = -15.440306509Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.440306509, -15.440306509}
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