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Simplifying 4x2 + 80x + -280 = 0 Reorder the terms: -280 + 80x + 4x2 = 0 Solving -280 + 80x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(-70 + 20x + x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-70 + 20x + x2)' equal to zero and attempt to solve: Simplifying -70 + 20x + x2 = 0 Solving -70 + 20x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '70' to each side of the equation. -70 + 20x + 70 + x2 = 0 + 70 Reorder the terms: -70 + 70 + 20x + x2 = 0 + 70 Combine like terms: -70 + 70 = 0 0 + 20x + x2 = 0 + 70 20x + x2 = 0 + 70 Combine like terms: 0 + 70 = 70 20x + x2 = 70 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 = 70 + 100 Reorder the terms: 100 + 20x + x2 = 70 + 100 Combine like terms: 70 + 100 = 170 100 + 20x + x2 = 170 Factor a perfect square on the left side: (x + 10)(x + 10) = 170 Calculate the square root of the right side: 13.03840481 Break this problem into two subproblems by setting (x + 10) equal to 13.03840481 and -13.03840481.Subproblem 1
x + 10 = 13.03840481 Simplifying x + 10 = 13.03840481 Reorder the terms: 10 + x = 13.03840481 Solving 10 + x = 13.03840481 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 = 13.03840481 + -10 Combine like terms: 10 + -10 = 0 0 + x = 13.03840481 + -10 x = 13.03840481 + -10 Combine like terms: 13.03840481 + -10 = 3.03840481 x = 3.03840481 Simplifying x = 3.03840481Subproblem 2
x + 10 = -13.03840481 Simplifying x + 10 = -13.03840481 Reorder the terms: 10 + x = -13.03840481 Solving 10 + x = -13.03840481 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 = -13.03840481 + -10 Combine like terms: 10 + -10 = 0 0 + x = -13.03840481 + -10 x = -13.03840481 + -10 Combine like terms: -13.03840481 + -10 = -23.03840481 x = -23.03840481 Simplifying x = -23.03840481Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.03840481, -23.03840481}Solution
x = {3.03840481, -23.03840481}
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