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Simplifying 2x2 + -40x + 10 = 0 Reorder the terms: 10 + -40x + 2x2 = 0 Solving 10 + -40x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(5 + -20x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(5 + -20x + x2)' equal to zero and attempt to solve: Simplifying 5 + -20x + x2 = 0 Solving 5 + -20x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-5' to each side of the equation. 5 + -20x + -5 + x2 = 0 + -5 Reorder the terms: 5 + -5 + -20x + x2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -20x + x2 = 0 + -5 -20x + x2 = 0 + -5 Combine like terms: 0 + -5 = -5 -20x + x2 = -5 The x term is -20x. Take half its coefficient (-10). Square it (100) and add it to both sides. Add '100' to each side of the equation. -20x + 100 + x2 = -5 + 100 Reorder the terms: 100 + -20x + x2 = -5 + 100 Combine like terms: -5 + 100 = 95 100 + -20x + x2 = 95 Factor a perfect square on the left side: (x + -10)(x + -10) = 95 Calculate the square root of the right side: 9.746794345 Break this problem into two subproblems by setting (x + -10) equal to 9.746794345 and -9.746794345.Subproblem 1
x + -10 = 9.746794345 Simplifying x + -10 = 9.746794345 Reorder the terms: -10 + x = 9.746794345 Solving -10 + x = 9.746794345 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = 9.746794345 + 10 Combine like terms: -10 + 10 = 0 0 + x = 9.746794345 + 10 x = 9.746794345 + 10 Combine like terms: 9.746794345 + 10 = 19.746794345 x = 19.746794345 Simplifying x = 19.746794345Subproblem 2
x + -10 = -9.746794345 Simplifying x + -10 = -9.746794345 Reorder the terms: -10 + x = -9.746794345 Solving -10 + x = -9.746794345 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = -9.746794345 + 10 Combine like terms: -10 + 10 = 0 0 + x = -9.746794345 + 10 x = -9.746794345 + 10 Combine like terms: -9.746794345 + 10 = 0.253205655 x = 0.253205655 Simplifying x = 0.253205655Solution
The solution to the problem is based on the solutions from the subproblems. x = {19.746794345, 0.253205655}Solution
x = {19.746794345, 0.253205655}
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