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Simplifying 4x + 110 = x2 + x Reorder the terms: 110 + 4x = x2 + x Reorder the terms: 110 + 4x = x + x2 Solving 110 + 4x = x + x2 Solving for variable 'x'. Combine like terms: 4x + -1x = 3x 110 + 3x + -1x2 = x + x2 + -1x + -1x2 Reorder the terms: 110 + 3x + -1x2 = x + -1x + x2 + -1x2 Combine like terms: x + -1x = 0 110 + 3x + -1x2 = 0 + x2 + -1x2 110 + 3x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 110 + 3x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -110 + -3x + x2 = 0 Move the constant term to the right: Add '110' to each side of the equation. -110 + -3x + 110 + x2 = 0 + 110 Reorder the terms: -110 + 110 + -3x + x2 = 0 + 110 Combine like terms: -110 + 110 = 0 0 + -3x + x2 = 0 + 110 -3x + x2 = 0 + 110 Combine like terms: 0 + 110 = 110 -3x + x2 = 110 The x term is -3x. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3x + 2.25 + x2 = 110 + 2.25 Reorder the terms: 2.25 + -3x + x2 = 110 + 2.25 Combine like terms: 110 + 2.25 = 112.25 2.25 + -3x + x2 = 112.25 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 112.25 Calculate the square root of the right side: 10.59481005 Break this problem into two subproblems by setting (x + -1.5) equal to 10.59481005 and -10.59481005.Subproblem 1
x + -1.5 = 10.59481005 Simplifying x + -1.5 = 10.59481005 Reorder the terms: -1.5 + x = 10.59481005 Solving -1.5 + x = 10.59481005 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = 10.59481005 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 10.59481005 + 1.5 x = 10.59481005 + 1.5 Combine like terms: 10.59481005 + 1.5 = 12.09481005 x = 12.09481005 Simplifying x = 12.09481005Subproblem 2
x + -1.5 = -10.59481005 Simplifying x + -1.5 = -10.59481005 Reorder the terms: -1.5 + x = -10.59481005 Solving -1.5 + x = -10.59481005 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = -10.59481005 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -10.59481005 + 1.5 x = -10.59481005 + 1.5 Combine like terms: -10.59481005 + 1.5 = -9.09481005 x = -9.09481005 Simplifying x = -9.09481005Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.09481005, -9.09481005}
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