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Simplifying 367 = 20x + 4x2 Solving 367 = 20x + 4x2 Solving for variable 'x'. Reorder the terms: 367 + -20x + -4x2 = 20x + -20x + 4x2 + -4x2 Combine like terms: 20x + -20x = 0 367 + -20x + -4x2 = 0 + 4x2 + -4x2 367 + -20x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 367 + -20x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -91.75 + 5x + x2 = 0 Move the constant term to the right: Add '91.75' to each side of the equation. -91.75 + 5x + 91.75 + x2 = 0 + 91.75 Reorder the terms: -91.75 + 91.75 + 5x + x2 = 0 + 91.75 Combine like terms: -91.75 + 91.75 = 0.00 0.00 + 5x + x2 = 0 + 91.75 5x + x2 = 0 + 91.75 Combine like terms: 0 + 91.75 = 91.75 5x + x2 = 91.75 The x term is 5x. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5x + 6.25 + x2 = 91.75 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 91.75 + 6.25 Combine like terms: 91.75 + 6.25 = 98 6.25 + 5x + x2 = 98 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 98 Calculate the square root of the right side: 9.899494937 Break this problem into two subproblems by setting (x + 2.5) equal to 9.899494937 and -9.899494937.Subproblem 1
x + 2.5 = 9.899494937 Simplifying x + 2.5 = 9.899494937 Reorder the terms: 2.5 + x = 9.899494937 Solving 2.5 + x = 9.899494937 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 9.899494937 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 9.899494937 + -2.5 x = 9.899494937 + -2.5 Combine like terms: 9.899494937 + -2.5 = 7.399494937 x = 7.399494937 Simplifying x = 7.399494937Subproblem 2
x + 2.5 = -9.899494937 Simplifying x + 2.5 = -9.899494937 Reorder the terms: 2.5 + x = -9.899494937 Solving 2.5 + x = -9.899494937 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -9.899494937 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -9.899494937 + -2.5 x = -9.899494937 + -2.5 Combine like terms: -9.899494937 + -2.5 = -12.399494937 x = -12.399494937 Simplifying x = -12.399494937Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.399494937, -12.399494937}
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