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Simplifying 5x2 + -65x + 25 = 0 Reorder the terms: 25 + -65x + 5x2 = 0 Solving 25 + -65x + 5x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '5'. 5(5 + -13x + x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(5 + -13x + x2)' equal to zero and attempt to solve: Simplifying 5 + -13x + x2 = 0 Solving 5 + -13x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-5' to each side of the equation. 5 + -13x + -5 + x2 = 0 + -5 Reorder the terms: 5 + -5 + -13x + x2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -13x + x2 = 0 + -5 -13x + x2 = 0 + -5 Combine like terms: 0 + -5 = -5 -13x + x2 = -5 The x term is -13x. Take half its coefficient (-6.5). Square it (42.25) and add it to both sides. Add '42.25' to each side of the equation. -13x + 42.25 + x2 = -5 + 42.25 Reorder the terms: 42.25 + -13x + x2 = -5 + 42.25 Combine like terms: -5 + 42.25 = 37.25 42.25 + -13x + x2 = 37.25 Factor a perfect square on the left side: (x + -6.5)(x + -6.5) = 37.25 Calculate the square root of the right side: 6.103277808 Break this problem into two subproblems by setting (x + -6.5) equal to 6.103277808 and -6.103277808.Subproblem 1
x + -6.5 = 6.103277808 Simplifying x + -6.5 = 6.103277808 Reorder the terms: -6.5 + x = 6.103277808 Solving -6.5 + x = 6.103277808 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + x = 6.103277808 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + x = 6.103277808 + 6.5 x = 6.103277808 + 6.5 Combine like terms: 6.103277808 + 6.5 = 12.603277808 x = 12.603277808 Simplifying x = 12.603277808Subproblem 2
x + -6.5 = -6.103277808 Simplifying x + -6.5 = -6.103277808 Reorder the terms: -6.5 + x = -6.103277808 Solving -6.5 + x = -6.103277808 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + x = -6.103277808 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + x = -6.103277808 + 6.5 x = -6.103277808 + 6.5 Combine like terms: -6.103277808 + 6.5 = 0.396722192 x = 0.396722192 Simplifying x = 0.396722192Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.603277808, 0.396722192}Solution
x = {12.603277808, 0.396722192}
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