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Simplifying 400 = 20x2 + 240x Reorder the terms: 400 = 240x + 20x2 Solving 400 = 240x + 20x2 Solving for variable 'x'. Reorder the terms: 400 + -240x + -20x2 = 240x + -240x + 20x2 + -20x2 Combine like terms: 240x + -240x = 0 400 + -240x + -20x2 = 0 + 20x2 + -20x2 400 + -240x + -20x2 = 20x2 + -20x2 Combine like terms: 20x2 + -20x2 = 0 400 + -240x + -20x2 = 0 Factor out the Greatest Common Factor (GCF), '20'. 20(20 + -12x + -1x2) = 0 Ignore the factor 20.Subproblem 1
Set the factor '(20 + -12x + -1x2)' equal to zero and attempt to solve: Simplifying 20 + -12x + -1x2 = 0 Solving 20 + -12x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -20 + 12x + x2 = 0 Move the constant term to the right: Add '20' to each side of the equation. -20 + 12x + 20 + x2 = 0 + 20 Reorder the terms: -20 + 20 + 12x + x2 = 0 + 20 Combine like terms: -20 + 20 = 0 0 + 12x + x2 = 0 + 20 12x + x2 = 0 + 20 Combine like terms: 0 + 20 = 20 12x + x2 = 20 The x term is 12x. Take half its coefficient (6). Square it (36) and add it to both sides. Add '36' to each side of the equation. 12x + 36 + x2 = 20 + 36 Reorder the terms: 36 + 12x + x2 = 20 + 36 Combine like terms: 20 + 36 = 56 36 + 12x + x2 = 56 Factor a perfect square on the left side: (x + 6)(x + 6) = 56 Calculate the square root of the right side: 7.483314774 Break this problem into two subproblems by setting (x + 6) equal to 7.483314774 and -7.483314774.Subproblem 1
x + 6 = 7.483314774 Simplifying x + 6 = 7.483314774 Reorder the terms: 6 + x = 7.483314774 Solving 6 + x = 7.483314774 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = 7.483314774 + -6 Combine like terms: 6 + -6 = 0 0 + x = 7.483314774 + -6 x = 7.483314774 + -6 Combine like terms: 7.483314774 + -6 = 1.483314774 x = 1.483314774 Simplifying x = 1.483314774Subproblem 2
x + 6 = -7.483314774 Simplifying x + 6 = -7.483314774 Reorder the terms: 6 + x = -7.483314774 Solving 6 + x = -7.483314774 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = -7.483314774 + -6 Combine like terms: 6 + -6 = 0 0 + x = -7.483314774 + -6 x = -7.483314774 + -6 Combine like terms: -7.483314774 + -6 = -13.483314774 x = -13.483314774 Simplifying x = -13.483314774Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.483314774, -13.483314774}Solution
x = {1.483314774, -13.483314774}
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