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Simplifying 2x2 + 40x + 100 = 0 Reorder the terms: 100 + 40x + 2x2 = 0 Solving 100 + 40x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(50 + 20x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(50 + 20x + x2)' equal to zero and attempt to solve: Simplifying 50 + 20x + x2 = 0 Solving 50 + 20x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-50' to each side of the equation. 50 + 20x + -50 + x2 = 0 + -50 Reorder the terms: 50 + -50 + 20x + x2 = 0 + -50 Combine like terms: 50 + -50 = 0 0 + 20x + x2 = 0 + -50 20x + x2 = 0 + -50 Combine like terms: 0 + -50 = -50 20x + x2 = -50 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 = -50 + 100 Reorder the terms: 100 + 20x + x2 = -50 + 100 Combine like terms: -50 + 100 = 50 100 + 20x + x2 = 50 Factor a perfect square on the left side: (x + 10)(x + 10) = 50 Calculate the square root of the right side: 7.071067812 Break this problem into two subproblems by setting (x + 10) equal to 7.071067812 and -7.071067812.Subproblem 1
x + 10 = 7.071067812 Simplifying x + 10 = 7.071067812 Reorder the terms: 10 + x = 7.071067812 Solving 10 + x = 7.071067812 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 = 7.071067812 + -10 Combine like terms: 10 + -10 = 0 0 + x = 7.071067812 + -10 x = 7.071067812 + -10 Combine like terms: 7.071067812 + -10 = -2.928932188 x = -2.928932188 Simplifying x = -2.928932188Subproblem 2
x + 10 = -7.071067812 Simplifying x + 10 = -7.071067812 Reorder the terms: 10 + x = -7.071067812 Solving 10 + x = -7.071067812 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 = -7.071067812 + -10 Combine like terms: 10 + -10 = 0 0 + x = -7.071067812 + -10 x = -7.071067812 + -10 Combine like terms: -7.071067812 + -10 = -17.071067812 x = -17.071067812 Simplifying x = -17.071067812Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.928932188, -17.071067812}Solution
x = {-2.928932188, -17.071067812}
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