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Simplifying -5x2 + 100x + 4000 = 40 Reorder the terms: 4000 + 100x + -5x2 = 40 Solving 4000 + 100x + -5x2 = 40 Solving for variable 'x'. Reorder the terms: 4000 + -40 + 100x + -5x2 = 40 + -40 Combine like terms: 4000 + -40 = 3960 3960 + 100x + -5x2 = 40 + -40 Combine like terms: 40 + -40 = 0 3960 + 100x + -5x2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(792 + 20x + -1x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(792 + 20x + -1x2)' equal to zero and attempt to solve: Simplifying 792 + 20x + -1x2 = 0 Solving 792 + 20x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -792 + -20x + x2 = 0 Move the constant term to the right: Add '792' to each side of the equation. -792 + -20x + 792 + x2 = 0 + 792 Reorder the terms: -792 + 792 + -20x + x2 = 0 + 792 Combine like terms: -792 + 792 = 0 0 + -20x + x2 = 0 + 792 -20x + x2 = 0 + 792 Combine like terms: 0 + 792 = 792 -20x + x2 = 792 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 = 792 + 100 Reorder the terms: 100 + -20x + x2 = 792 + 100 Combine like terms: 792 + 100 = 892 100 + -20x + x2 = 892 Factor a perfect square on the left side: (x + -10)(x + -10) = 892 Calculate the square root of the right side: 29.866369046 Break this problem into two subproblems by setting (x + -10) equal to 29.866369046 and -29.866369046.Subproblem 1
x + -10 = 29.866369046 Simplifying x + -10 = 29.866369046 Reorder the terms: -10 + x = 29.866369046 Solving -10 + x = 29.866369046 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 = 29.866369046 + 10 Combine like terms: -10 + 10 = 0 0 + x = 29.866369046 + 10 x = 29.866369046 + 10 Combine like terms: 29.866369046 + 10 = 39.866369046 x = 39.866369046 Simplifying x = 39.866369046Subproblem 2
x + -10 = -29.866369046 Simplifying x + -10 = -29.866369046 Reorder the terms: -10 + x = -29.866369046 Solving -10 + x = -29.866369046 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 = -29.866369046 + 10 Combine like terms: -10 + 10 = 0 0 + x = -29.866369046 + 10 x = -29.866369046 + 10 Combine like terms: -29.866369046 + 10 = -19.866369046 x = -19.866369046 Simplifying x = -19.866369046Solution
The solution to the problem is based on the solutions from the subproblems. x = {39.866369046, -19.866369046}Solution
x = {39.866369046, -19.866369046}
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