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Simplifying -10x2 + 380x + 80 = 0 Reorder the terms: 80 + 380x + -10x2 = 0 Solving 80 + 380x + -10x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '10'. 10(8 + 38x + -1x2) = 0 Ignore the factor 10.Subproblem 1
Set the factor '(8 + 38x + -1x2)' equal to zero and attempt to solve: Simplifying 8 + 38x + -1x2 = 0 Solving 8 + 38x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -8 + -38x + x2 = 0 Move the constant term to the right: Add '8' to each side of the equation. -8 + -38x + 8 + x2 = 0 + 8 Reorder the terms: -8 + 8 + -38x + x2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -38x + x2 = 0 + 8 -38x + x2 = 0 + 8 Combine like terms: 0 + 8 = 8 -38x + x2 = 8 The x term is -38x. Take half its coefficient (-19). Square it (361) and add it to both sides. Add '361' to each side of the equation. -38x + 361 + x2 = 8 + 361 Reorder the terms: 361 + -38x + x2 = 8 + 361 Combine like terms: 8 + 361 = 369 361 + -38x + x2 = 369 Factor a perfect square on the left side: (x + -19)(x + -19) = 369 Calculate the square root of the right side: 19.209372712 Break this problem into two subproblems by setting (x + -19) equal to 19.209372712 and -19.209372712.Subproblem 1
x + -19 = 19.209372712 Simplifying x + -19 = 19.209372712 Reorder the terms: -19 + x = 19.209372712 Solving -19 + x = 19.209372712 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '19' to each side of the equation. -19 + 19 + x = 19.209372712 + 19 Combine like terms: -19 + 19 = 0 0 + x = 19.209372712 + 19 x = 19.209372712 + 19 Combine like terms: 19.209372712 + 19 = 38.209372712 x = 38.209372712 Simplifying x = 38.209372712Subproblem 2
x + -19 = -19.209372712 Simplifying x + -19 = -19.209372712 Reorder the terms: -19 + x = -19.209372712 Solving -19 + x = -19.209372712 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '19' to each side of the equation. -19 + 19 + x = -19.209372712 + 19 Combine like terms: -19 + 19 = 0 0 + x = -19.209372712 + 19 x = -19.209372712 + 19 Combine like terms: -19.209372712 + 19 = -0.209372712 x = -0.209372712 Simplifying x = -0.209372712Solution
The solution to the problem is based on the solutions from the subproblems. x = {38.209372712, -0.209372712}Solution
x = {38.209372712, -0.209372712}
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