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Simplifying 100 = 6x + x2 Solving 100 = 6x + x2 Solving for variable 'x'. Reorder the terms: 100 + -6x + -1x2 = 6x + -6x + x2 + -1x2 Combine like terms: 6x + -6x = 0 100 + -6x + -1x2 = 0 + x2 + -1x2 100 + -6x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 100 + -6x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -100 + 6x + x2 = 0 Move the constant term to the right: Add '100' to each side of the equation. -100 + 6x + 100 + x2 = 0 + 100 Reorder the terms: -100 + 100 + 6x + x2 = 0 + 100 Combine like terms: -100 + 100 = 0 0 + 6x + x2 = 0 + 100 6x + x2 = 0 + 100 Combine like terms: 0 + 100 = 100 6x + x2 = 100 The x term is 6x. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x + 9 + x2 = 100 + 9 Reorder the terms: 9 + 6x + x2 = 100 + 9 Combine like terms: 100 + 9 = 109 9 + 6x + x2 = 109 Factor a perfect square on the left side: (x + 3)(x + 3) = 109 Calculate the square root of the right side: 10.440306509 Break this problem into two subproblems by setting (x + 3) equal to 10.440306509 and -10.440306509.Subproblem 1
x + 3 = 10.440306509 Simplifying x + 3 = 10.440306509 Reorder the terms: 3 + x = 10.440306509 Solving 3 + x = 10.440306509 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 10.440306509 + -3 Combine like terms: 3 + -3 = 0 0 + x = 10.440306509 + -3 x = 10.440306509 + -3 Combine like terms: 10.440306509 + -3 = 7.440306509 x = 7.440306509 Simplifying x = 7.440306509Subproblem 2
x + 3 = -10.440306509 Simplifying x + 3 = -10.440306509 Reorder the terms: 3 + x = -10.440306509 Solving 3 + x = -10.440306509 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -10.440306509 + -3 Combine like terms: 3 + -3 = 0 0 + x = -10.440306509 + -3 x = -10.440306509 + -3 Combine like terms: -10.440306509 + -3 = -13.440306509 x = -13.440306509 Simplifying x = -13.440306509Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.440306509, -13.440306509}
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