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Simplifying 5x2 + -65x + -10 = 0 Reorder the terms: -10 + -65x + 5x2 = 0 Solving -10 + -65x + 5x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '5'. 5(-2 + -13x + x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-2 + -13x + x2)' equal to zero and attempt to solve: Simplifying -2 + -13x + x2 = 0 Solving -2 + -13x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '2' to each side of the equation. -2 + -13x + 2 + x2 = 0 + 2 Reorder the terms: -2 + 2 + -13x + x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -13x + x2 = 0 + 2 -13x + x2 = 0 + 2 Combine like terms: 0 + 2 = 2 -13x + x2 = 2 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 = 2 + 42.25 Reorder the terms: 42.25 + -13x + x2 = 2 + 42.25 Combine like terms: 2 + 42.25 = 44.25 42.25 + -13x + x2 = 44.25 Factor a perfect square on the left side: (x + -6.5)(x + -6.5) = 44.25 Calculate the square root of the right side: 6.652067348 Break this problem into two subproblems by setting (x + -6.5) equal to 6.652067348 and -6.652067348.Subproblem 1
x + -6.5 = 6.652067348 Simplifying x + -6.5 = 6.652067348 Reorder the terms: -6.5 + x = 6.652067348 Solving -6.5 + x = 6.652067348 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 = 6.652067348 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + x = 6.652067348 + 6.5 x = 6.652067348 + 6.5 Combine like terms: 6.652067348 + 6.5 = 13.152067348 x = 13.152067348 Simplifying x = 13.152067348Subproblem 2
x + -6.5 = -6.652067348 Simplifying x + -6.5 = -6.652067348 Reorder the terms: -6.5 + x = -6.652067348 Solving -6.5 + x = -6.652067348 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 = -6.652067348 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + x = -6.652067348 + 6.5 x = -6.652067348 + 6.5 Combine like terms: -6.652067348 + 6.5 = -0.152067348 x = -0.152067348 Simplifying x = -0.152067348Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.152067348, -0.152067348}Solution
x = {13.152067348, -0.152067348}
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