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Simplifying 5x2 + -105x + 105 = 0 Reorder the terms: 105 + -105x + 5x2 = 0 Solving 105 + -105x + 5x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '5'. 5(21 + -21x + x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(21 + -21x + x2)' equal to zero and attempt to solve: Simplifying 21 + -21x + x2 = 0 Solving 21 + -21x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-21' to each side of the equation. 21 + -21x + -21 + x2 = 0 + -21 Reorder the terms: 21 + -21 + -21x + x2 = 0 + -21 Combine like terms: 21 + -21 = 0 0 + -21x + x2 = 0 + -21 -21x + x2 = 0 + -21 Combine like terms: 0 + -21 = -21 -21x + x2 = -21 The x term is -21x. Take half its coefficient (-10.5). Square it (110.25) and add it to both sides. Add '110.25' to each side of the equation. -21x + 110.25 + x2 = -21 + 110.25 Reorder the terms: 110.25 + -21x + x2 = -21 + 110.25 Combine like terms: -21 + 110.25 = 89.25 110.25 + -21x + x2 = 89.25 Factor a perfect square on the left side: (x + -10.5)(x + -10.5) = 89.25 Calculate the square root of the right side: 9.447221814 Break this problem into two subproblems by setting (x + -10.5) equal to 9.447221814 and -9.447221814.Subproblem 1
x + -10.5 = 9.447221814 Simplifying x + -10.5 = 9.447221814 Reorder the terms: -10.5 + x = 9.447221814 Solving -10.5 + x = 9.447221814 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10.5' to each side of the equation. -10.5 + 10.5 + x = 9.447221814 + 10.5 Combine like terms: -10.5 + 10.5 = 0.0 0.0 + x = 9.447221814 + 10.5 x = 9.447221814 + 10.5 Combine like terms: 9.447221814 + 10.5 = 19.947221814 x = 19.947221814 Simplifying x = 19.947221814Subproblem 2
x + -10.5 = -9.447221814 Simplifying x + -10.5 = -9.447221814 Reorder the terms: -10.5 + x = -9.447221814 Solving -10.5 + x = -9.447221814 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10.5' to each side of the equation. -10.5 + 10.5 + x = -9.447221814 + 10.5 Combine like terms: -10.5 + 10.5 = 0.0 0.0 + x = -9.447221814 + 10.5 x = -9.447221814 + 10.5 Combine like terms: -9.447221814 + 10.5 = 1.052778186 x = 1.052778186 Simplifying x = 1.052778186Solution
The solution to the problem is based on the solutions from the subproblems. x = {19.947221814, 1.052778186}Solution
x = {19.947221814, 1.052778186}
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