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Simplifying 2x2 + 20x + -884 = 0 Reorder the terms: -884 + 20x + 2x2 = 0 Solving -884 + 20x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-442 + 10x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-442 + 10x + x2)' equal to zero and attempt to solve: Simplifying -442 + 10x + x2 = 0 Solving -442 + 10x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '442' to each side of the equation. -442 + 10x + 442 + x2 = 0 + 442 Reorder the terms: -442 + 442 + 10x + x2 = 0 + 442 Combine like terms: -442 + 442 = 0 0 + 10x + x2 = 0 + 442 10x + x2 = 0 + 442 Combine like terms: 0 + 442 = 442 10x + x2 = 442 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 = 442 + 25 Reorder the terms: 25 + 10x + x2 = 442 + 25 Combine like terms: 442 + 25 = 467 25 + 10x + x2 = 467 Factor a perfect square on the left side: (x + 5)(x + 5) = 467 Calculate the square root of the right side: 21.610182785 Break this problem into two subproblems by setting (x + 5) equal to 21.610182785 and -21.610182785.Subproblem 1
x + 5 = 21.610182785 Simplifying x + 5 = 21.610182785 Reorder the terms: 5 + x = 21.610182785 Solving 5 + x = 21.610182785 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 = 21.610182785 + -5 Combine like terms: 5 + -5 = 0 0 + x = 21.610182785 + -5 x = 21.610182785 + -5 Combine like terms: 21.610182785 + -5 = 16.610182785 x = 16.610182785 Simplifying x = 16.610182785Subproblem 2
x + 5 = -21.610182785 Simplifying x + 5 = -21.610182785 Reorder the terms: 5 + x = -21.610182785 Solving 5 + x = -21.610182785 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 = -21.610182785 + -5 Combine like terms: 5 + -5 = 0 0 + x = -21.610182785 + -5 x = -21.610182785 + -5 Combine like terms: -21.610182785 + -5 = -26.610182785 x = -26.610182785 Simplifying x = -26.610182785Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.610182785, -26.610182785}Solution
x = {16.610182785, -26.610182785}
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