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Simplifying 2x2 + 4.2x + -146.88 = 0 Reorder the terms: -146.88 + 4.2x + 2x2 = 0 Solving -146.88 + 4.2x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -73.44 + 2.1x + x2 = 0 Move the constant term to the right: Add '73.44' to each side of the equation. -73.44 + 2.1x + 73.44 + x2 = 0 + 73.44 Reorder the terms: -73.44 + 73.44 + 2.1x + x2 = 0 + 73.44 Combine like terms: -73.44 + 73.44 = 0.00 0.00 + 2.1x + x2 = 0 + 73.44 2.1x + x2 = 0 + 73.44 Combine like terms: 0 + 73.44 = 73.44 2.1x + x2 = 73.44 The x term is 2.1x. Take half its coefficient (1.05). Square it (1.1025) and add it to both sides. Add '1.1025' to each side of the equation. 2.1x + 1.1025 + x2 = 73.44 + 1.1025 Reorder the terms: 1.1025 + 2.1x + x2 = 73.44 + 1.1025 Combine like terms: 73.44 + 1.1025 = 74.5425 1.1025 + 2.1x + x2 = 74.5425 Factor a perfect square on the left side: (x + 1.05)(x + 1.05) = 74.5425 Calculate the square root of the right side: 8.633799859 Break this problem into two subproblems by setting (x + 1.05) equal to 8.633799859 and -8.633799859.Subproblem 1
x + 1.05 = 8.633799859 Simplifying x + 1.05 = 8.633799859 Reorder the terms: 1.05 + x = 8.633799859 Solving 1.05 + x = 8.633799859 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.05' to each side of the equation. 1.05 + -1.05 + x = 8.633799859 + -1.05 Combine like terms: 1.05 + -1.05 = 0.00 0.00 + x = 8.633799859 + -1.05 x = 8.633799859 + -1.05 Combine like terms: 8.633799859 + -1.05 = 7.583799859 x = 7.583799859 Simplifying x = 7.583799859Subproblem 2
x + 1.05 = -8.633799859 Simplifying x + 1.05 = -8.633799859 Reorder the terms: 1.05 + x = -8.633799859 Solving 1.05 + x = -8.633799859 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.05' to each side of the equation. 1.05 + -1.05 + x = -8.633799859 + -1.05 Combine like terms: 1.05 + -1.05 = 0.00 0.00 + x = -8.633799859 + -1.05 x = -8.633799859 + -1.05 Combine like terms: -8.633799859 + -1.05 = -9.683799859 x = -9.683799859 Simplifying x = -9.683799859Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.583799859, -9.683799859}
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