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Simplifying 2x2 + 20x + 10 = 0 Reorder the terms: 10 + 20x + 2x2 = 0 Solving 10 + 20x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(5 + 10x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(5 + 10x + x2)' equal to zero and attempt to solve: Simplifying 5 + 10x + x2 = 0 Solving 5 + 10x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-5' to each side of the equation. 5 + 10x + -5 + x2 = 0 + -5 Reorder the terms: 5 + -5 + 10x + x2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 10x + x2 = 0 + -5 10x + x2 = 0 + -5 Combine like terms: 0 + -5 = -5 10x + x2 = -5 The x term is 10x. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10x + 25 + x2 = -5 + 25 Reorder the terms: 25 + 10x + x2 = -5 + 25 Combine like terms: -5 + 25 = 20 25 + 10x + x2 = 20 Factor a perfect square on the left side: (x + 5)(x + 5) = 20 Calculate the square root of the right side: 4.472135955 Break this problem into two subproblems by setting (x + 5) equal to 4.472135955 and -4.472135955.Subproblem 1
x + 5 = 4.472135955 Simplifying x + 5 = 4.472135955 Reorder the terms: 5 + x = 4.472135955 Solving 5 + x = 4.472135955 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 4.472135955 + -5 Combine like terms: 5 + -5 = 0 0 + x = 4.472135955 + -5 x = 4.472135955 + -5 Combine like terms: 4.472135955 + -5 = -0.527864045 x = -0.527864045 Simplifying x = -0.527864045Subproblem 2
x + 5 = -4.472135955 Simplifying x + 5 = -4.472135955 Reorder the terms: 5 + x = -4.472135955 Solving 5 + x = -4.472135955 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = -4.472135955 + -5 Combine like terms: 5 + -5 = 0 0 + x = -4.472135955 + -5 x = -4.472135955 + -5 Combine like terms: -4.472135955 + -5 = -9.472135955 x = -9.472135955 Simplifying x = -9.472135955Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.527864045, -9.472135955}Solution
x = {-0.527864045, -9.472135955}
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