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Simplifying 73x + -2x2 = 25x + 108 Reorder the terms: 73x + -2x2 = 108 + 25x Solving 73x + -2x2 = 108 + 25x Solving for variable 'x'. Reorder the terms: -108 + 73x + -25x + -2x2 = 108 + 25x + -108 + -25x Combine like terms: 73x + -25x = 48x -108 + 48x + -2x2 = 108 + 25x + -108 + -25x Reorder the terms: -108 + 48x + -2x2 = 108 + -108 + 25x + -25x Combine like terms: 108 + -108 = 0 -108 + 48x + -2x2 = 0 + 25x + -25x -108 + 48x + -2x2 = 25x + -25x Combine like terms: 25x + -25x = 0 -108 + 48x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-54 + 24x + -1x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-54 + 24x + -1x2)' equal to zero and attempt to solve: Simplifying -54 + 24x + -1x2 = 0 Solving -54 + 24x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 54 + -24x + x2 = 0 Move the constant term to the right: Add '-54' to each side of the equation. 54 + -24x + -54 + x2 = 0 + -54 Reorder the terms: 54 + -54 + -24x + x2 = 0 + -54 Combine like terms: 54 + -54 = 0 0 + -24x + x2 = 0 + -54 -24x + x2 = 0 + -54 Combine like terms: 0 + -54 = -54 -24x + x2 = -54 The x term is -24x. Take half its coefficient (-12). Square it (144) and add it to both sides. Add '144' to each side of the equation. -24x + 144 + x2 = -54 + 144 Reorder the terms: 144 + -24x + x2 = -54 + 144 Combine like terms: -54 + 144 = 90 144 + -24x + x2 = 90 Factor a perfect square on the left side: (x + -12)(x + -12) = 90 Calculate the square root of the right side: 9.486832981 Break this problem into two subproblems by setting (x + -12) equal to 9.486832981 and -9.486832981.Subproblem 1
x + -12 = 9.486832981 Simplifying x + -12 = 9.486832981 Reorder the terms: -12 + x = 9.486832981 Solving -12 + x = 9.486832981 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + x = 9.486832981 + 12 Combine like terms: -12 + 12 = 0 0 + x = 9.486832981 + 12 x = 9.486832981 + 12 Combine like terms: 9.486832981 + 12 = 21.486832981 x = 21.486832981 Simplifying x = 21.486832981Subproblem 2
x + -12 = -9.486832981 Simplifying x + -12 = -9.486832981 Reorder the terms: -12 + x = -9.486832981 Solving -12 + x = -9.486832981 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + x = -9.486832981 + 12 Combine like terms: -12 + 12 = 0 0 + x = -9.486832981 + 12 x = -9.486832981 + 12 Combine like terms: -9.486832981 + 12 = 2.513167019 x = 2.513167019 Simplifying x = 2.513167019Solution
The solution to the problem is based on the solutions from the subproblems. x = {21.486832981, 2.513167019}Solution
x = {21.486832981, 2.513167019}
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