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Simplifying 5x2 + -75x + -15 = 0 Reorder the terms: -15 + -75x + 5x2 = 0 Solving -15 + -75x + 5x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '5'. 5(-3 + -15x + x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-3 + -15x + x2)' equal to zero and attempt to solve: Simplifying -3 + -15x + x2 = 0 Solving -3 + -15x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '3' to each side of the equation. -3 + -15x + 3 + x2 = 0 + 3 Reorder the terms: -3 + 3 + -15x + x2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -15x + x2 = 0 + 3 -15x + x2 = 0 + 3 Combine like terms: 0 + 3 = 3 -15x + x2 = 3 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 = 3 + 56.25 Reorder the terms: 56.25 + -15x + x2 = 3 + 56.25 Combine like terms: 3 + 56.25 = 59.25 56.25 + -15x + x2 = 59.25 Factor a perfect square on the left side: (x + -7.5)(x + -7.5) = 59.25 Calculate the square root of the right side: 7.697402159 Break this problem into two subproblems by setting (x + -7.5) equal to 7.697402159 and -7.697402159.Subproblem 1
x + -7.5 = 7.697402159 Simplifying x + -7.5 = 7.697402159 Reorder the terms: -7.5 + x = 7.697402159 Solving -7.5 + x = 7.697402159 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 = 7.697402159 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = 7.697402159 + 7.5 x = 7.697402159 + 7.5 Combine like terms: 7.697402159 + 7.5 = 15.197402159 x = 15.197402159 Simplifying x = 15.197402159Subproblem 2
x + -7.5 = -7.697402159 Simplifying x + -7.5 = -7.697402159 Reorder the terms: -7.5 + x = -7.697402159 Solving -7.5 + x = -7.697402159 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 = -7.697402159 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = -7.697402159 + 7.5 x = -7.697402159 + 7.5 Combine like terms: -7.697402159 + 7.5 = -0.197402159 x = -0.197402159 Simplifying x = -0.197402159Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.197402159, -0.197402159}Solution
x = {15.197402159, -0.197402159}
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