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Simplifying 5x2 + -75x + 260 = 0 Reorder the terms: 260 + -75x + 5x2 = 0 Solving 260 + -75x + 5x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '5'. 5(52 + -15x + x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(52 + -15x + x2)' equal to zero and attempt to solve: Simplifying 52 + -15x + x2 = 0 Solving 52 + -15x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-52' to each side of the equation. 52 + -15x + -52 + x2 = 0 + -52 Reorder the terms: 52 + -52 + -15x + x2 = 0 + -52 Combine like terms: 52 + -52 = 0 0 + -15x + x2 = 0 + -52 -15x + x2 = 0 + -52 Combine like terms: 0 + -52 = -52 -15x + x2 = -52 The x term is -15x. Take half its coefficient (-7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. -15x + 56.25 + x2 = -52 + 56.25 Reorder the terms: 56.25 + -15x + x2 = -52 + 56.25 Combine like terms: -52 + 56.25 = 4.25 56.25 + -15x + x2 = 4.25 Factor a perfect square on the left side: (x + -7.5)(x + -7.5) = 4.25 Calculate the square root of the right side: 2.061552813 Break this problem into two subproblems by setting (x + -7.5) equal to 2.061552813 and -2.061552813.Subproblem 1
x + -7.5 = 2.061552813 Simplifying x + -7.5 = 2.061552813 Reorder the terms: -7.5 + x = 2.061552813 Solving -7.5 + x = 2.061552813 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + x = 2.061552813 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = 2.061552813 + 7.5 x = 2.061552813 + 7.5 Combine like terms: 2.061552813 + 7.5 = 9.561552813 x = 9.561552813 Simplifying x = 9.561552813Subproblem 2
x + -7.5 = -2.061552813 Simplifying x + -7.5 = -2.061552813 Reorder the terms: -7.5 + x = -2.061552813 Solving -7.5 + x = -2.061552813 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + x = -2.061552813 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = -2.061552813 + 7.5 x = -2.061552813 + 7.5 Combine like terms: -2.061552813 + 7.5 = 5.438447187 x = 5.438447187 Simplifying x = 5.438447187Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.561552813, 5.438447187}Solution
x = {9.561552813, 5.438447187}
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