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Simplifying 4x + 110 = (x2 + 5) Reorder the terms: 110 + 4x = (x2 + 5) Reorder the terms: 110 + 4x = (5 + x2) Remove parenthesis around (5 + x2) 110 + 4x = 5 + x2 Solving 110 + 4x = 5 + x2 Solving for variable 'x'. Reorder the terms: 110 + -5 + 4x + -1x2 = 5 + x2 + -5 + -1x2 Combine like terms: 110 + -5 = 105 105 + 4x + -1x2 = 5 + x2 + -5 + -1x2 Reorder the terms: 105 + 4x + -1x2 = 5 + -5 + x2 + -1x2 Combine like terms: 5 + -5 = 0 105 + 4x + -1x2 = 0 + x2 + -1x2 105 + 4x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 105 + 4x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -105 + -4x + x2 = 0 Move the constant term to the right: Add '105' to each side of the equation. -105 + -4x + 105 + x2 = 0 + 105 Reorder the terms: -105 + 105 + -4x + x2 = 0 + 105 Combine like terms: -105 + 105 = 0 0 + -4x + x2 = 0 + 105 -4x + x2 = 0 + 105 Combine like terms: 0 + 105 = 105 -4x + x2 = 105 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = 105 + 4 Reorder the terms: 4 + -4x + x2 = 105 + 4 Combine like terms: 105 + 4 = 109 4 + -4x + x2 = 109 Factor a perfect square on the left side: (x + -2)(x + -2) = 109 Calculate the square root of the right side: 10.440306509 Break this problem into two subproblems by setting (x + -2) equal to 10.440306509 and -10.440306509.Subproblem 1
x + -2 = 10.440306509 Simplifying x + -2 = 10.440306509 Reorder the terms: -2 + x = 10.440306509 Solving -2 + x = 10.440306509 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 10.440306509 + 2 Combine like terms: -2 + 2 = 0 0 + x = 10.440306509 + 2 x = 10.440306509 + 2 Combine like terms: 10.440306509 + 2 = 12.440306509 x = 12.440306509 Simplifying x = 12.440306509Subproblem 2
x + -2 = -10.440306509 Simplifying x + -2 = -10.440306509 Reorder the terms: -2 + x = -10.440306509 Solving -2 + x = -10.440306509 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -10.440306509 + 2 Combine like terms: -2 + 2 = 0 0 + x = -10.440306509 + 2 x = -10.440306509 + 2 Combine like terms: -10.440306509 + 2 = -8.440306509 x = -8.440306509 Simplifying x = -8.440306509Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.440306509, -8.440306509}
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