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Simplifying 5x2 + -105x + 275 = 0 Reorder the terms: 275 + -105x + 5x2 = 0 Solving 275 + -105x + 5x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '5'. 5(55 + -21x + x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(55 + -21x + x2)' equal to zero and attempt to solve: Simplifying 55 + -21x + x2 = 0 Solving 55 + -21x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-55' to each side of the equation. 55 + -21x + -55 + x2 = 0 + -55 Reorder the terms: 55 + -55 + -21x + x2 = 0 + -55 Combine like terms: 55 + -55 = 0 0 + -21x + x2 = 0 + -55 -21x + x2 = 0 + -55 Combine like terms: 0 + -55 = -55 -21x + x2 = -55 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 = -55 + 110.25 Reorder the terms: 110.25 + -21x + x2 = -55 + 110.25 Combine like terms: -55 + 110.25 = 55.25 110.25 + -21x + x2 = 55.25 Factor a perfect square on the left side: (x + -10.5)(x + -10.5) = 55.25 Calculate the square root of the right side: 7.433034374 Break this problem into two subproblems by setting (x + -10.5) equal to 7.433034374 and -7.433034374.Subproblem 1
x + -10.5 = 7.433034374 Simplifying x + -10.5 = 7.433034374 Reorder the terms: -10.5 + x = 7.433034374 Solving -10.5 + x = 7.433034374 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 = 7.433034374 + 10.5 Combine like terms: -10.5 + 10.5 = 0.0 0.0 + x = 7.433034374 + 10.5 x = 7.433034374 + 10.5 Combine like terms: 7.433034374 + 10.5 = 17.933034374 x = 17.933034374 Simplifying x = 17.933034374Subproblem 2
x + -10.5 = -7.433034374 Simplifying x + -10.5 = -7.433034374 Reorder the terms: -10.5 + x = -7.433034374 Solving -10.5 + x = -7.433034374 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 = -7.433034374 + 10.5 Combine like terms: -10.5 + 10.5 = 0.0 0.0 + x = -7.433034374 + 10.5 x = -7.433034374 + 10.5 Combine like terms: -7.433034374 + 10.5 = 3.066965626 x = 3.066965626 Simplifying x = 3.066965626Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.933034374, 3.066965626}Solution
x = {17.933034374, 3.066965626}
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