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Simplifying 10.5x + 110.25 = x2 Reorder the terms: 110.25 + 10.5x = x2 Solving 110.25 + 10.5x = x2 Solving for variable 'x'. Combine like terms: x2 + -1x2 = 0 110.25 + 10.5x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -110.25 + -10.5x + x2 = 0 Move the constant term to the right: Add '110.25' to each side of the equation. -110.25 + -10.5x + 110.25 + x2 = 0 + 110.25 Reorder the terms: -110.25 + 110.25 + -10.5x + x2 = 0 + 110.25 Combine like terms: -110.25 + 110.25 = 0.00 0.00 + -10.5x + x2 = 0 + 110.25 -10.5x + x2 = 0 + 110.25 Combine like terms: 0 + 110.25 = 110.25 -10.5x + x2 = 110.25 The x term is -10.5x. Take half its coefficient (-5.25). Square it (27.5625) and add it to both sides. Add '27.5625' to each side of the equation. -10.5x + 27.5625 + x2 = 110.25 + 27.5625 Reorder the terms: 27.5625 + -10.5x + x2 = 110.25 + 27.5625 Combine like terms: 110.25 + 27.5625 = 137.8125 27.5625 + -10.5x + x2 = 137.8125 Factor a perfect square on the left side: (x + -5.25)(x + -5.25) = 137.8125 Calculate the square root of the right side: 11.739356882 Break this problem into two subproblems by setting (x + -5.25) equal to 11.739356882 and -11.739356882.Subproblem 1
x + -5.25 = 11.739356882 Simplifying x + -5.25 = 11.739356882 Reorder the terms: -5.25 + x = 11.739356882 Solving -5.25 + x = 11.739356882 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.25' to each side of the equation. -5.25 + 5.25 + x = 11.739356882 + 5.25 Combine like terms: -5.25 + 5.25 = 0.00 0.00 + x = 11.739356882 + 5.25 x = 11.739356882 + 5.25 Combine like terms: 11.739356882 + 5.25 = 16.989356882 x = 16.989356882 Simplifying x = 16.989356882Subproblem 2
x + -5.25 = -11.739356882 Simplifying x + -5.25 = -11.739356882 Reorder the terms: -5.25 + x = -11.739356882 Solving -5.25 + x = -11.739356882 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.25' to each side of the equation. -5.25 + 5.25 + x = -11.739356882 + 5.25 Combine like terms: -5.25 + 5.25 = 0.00 0.00 + x = -11.739356882 + 5.25 x = -11.739356882 + 5.25 Combine like terms: -11.739356882 + 5.25 = -6.489356882 x = -6.489356882 Simplifying x = -6.489356882Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.989356882, -6.489356882}
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