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Simplifying 4.9x2 + 330x + -3300 = 0 Reorder the terms: -3300 + 330x + 4.9x2 = 0 Solving -3300 + 330x + 4.9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4.9 the coefficient of the squared term: Divide each side by '4.9'. -673.4693878 + 67.34693878x + x2 = 0 Move the constant term to the right: Add '673.4693878' to each side of the equation. -673.4693878 + 67.34693878x + 673.4693878 + x2 = 0 + 673.4693878 Reorder the terms: -673.4693878 + 673.4693878 + 67.34693878x + x2 = 0 + 673.4693878 Combine like terms: -673.4693878 + 673.4693878 = 0.0000000 0.0000000 + 67.34693878x + x2 = 0 + 673.4693878 67.34693878x + x2 = 0 + 673.4693878 Combine like terms: 0 + 673.4693878 = 673.4693878 67.34693878x + x2 = 673.4693878 The x term is 67.34693878x. Take half its coefficient (33.67346939). Square it (1133.902541) and add it to both sides. Add '1133.902541' to each side of the equation. 67.34693878x + 1133.902541 + x2 = 673.4693878 + 1133.902541 Reorder the terms: 1133.902541 + 67.34693878x + x2 = 673.4693878 + 1133.902541 Combine like terms: 673.4693878 + 1133.902541 = 1807.3719288 1133.902541 + 67.34693878x + x2 = 1807.3719288 Factor a perfect square on the left side: (x + 33.67346939)(x + 33.67346939) = 1807.3719288 Calculate the square root of the right side: 42.513197113 Break this problem into two subproblems by setting (x + 33.67346939) equal to 42.513197113 and -42.513197113.Subproblem 1
x + 33.67346939 = 42.513197113 Simplifying x + 33.67346939 = 42.513197113 Reorder the terms: 33.67346939 + x = 42.513197113 Solving 33.67346939 + x = 42.513197113 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-33.67346939' to each side of the equation. 33.67346939 + -33.67346939 + x = 42.513197113 + -33.67346939 Combine like terms: 33.67346939 + -33.67346939 = 0.00000000 0.00000000 + x = 42.513197113 + -33.67346939 x = 42.513197113 + -33.67346939 Combine like terms: 42.513197113 + -33.67346939 = 8.839727723 x = 8.839727723 Simplifying x = 8.839727723Subproblem 2
x + 33.67346939 = -42.513197113 Simplifying x + 33.67346939 = -42.513197113 Reorder the terms: 33.67346939 + x = -42.513197113 Solving 33.67346939 + x = -42.513197113 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-33.67346939' to each side of the equation. 33.67346939 + -33.67346939 + x = -42.513197113 + -33.67346939 Combine like terms: 33.67346939 + -33.67346939 = 0.00000000 0.00000000 + x = -42.513197113 + -33.67346939 x = -42.513197113 + -33.67346939 Combine like terms: -42.513197113 + -33.67346939 = -76.186666503 x = -76.186666503 Simplifying x = -76.186666503Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.839727723, -76.186666503}
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