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Simplifying 7.94x2 + 33.2x + 2190 = 9000000000000 Reorder the terms: 2190 + 33.2x + 7.94x2 = 9000000000000 Solving 2190 + 33.2x + 7.94x2 = 9000000000000 Solving for variable 'x'. Reorder the terms: 2190 + -9000000000000 + 33.2x + 7.94x2 = 9000000000000 + -9000000000000 Combine like terms: 2190 + -9000000000000 = -8999999997810 -8999999997810 + 33.2x + 7.94x2 = 9000000000000 + -9000000000000 Combine like terms: 9000000000000 + -9000000000000 = 0 -8999999997810 + 33.2x + 7.94x2 = 0 Begin completing the square. Divide all terms by 7.94 the coefficient of the squared term: Divide each side by '7.94'. -1133501259000 + 4.181360202x + x2 = 0 Move the constant term to the right: Add '1133501259000' to each side of the equation. -1133501259000 + 4.181360202x + 1133501259000 + x2 = 0 + 1133501259000 Reorder the terms: -1133501259000 + 1133501259000 + 4.181360202x + x2 = 0 + 1133501259000 Combine like terms: -1133501259000 + 1133501259000 = 0 0 + 4.181360202x + x2 = 0 + 1133501259000 4.181360202x + x2 = 0 + 1133501259000 Combine like terms: 0 + 1133501259000 = 1133501259000 4.181360202x + x2 = 1133501259000 The x term is 4.181360202x. Take half its coefficient (2.090680101). Square it (4.370943285) and add it to both sides. Add '4.370943285' to each side of the equation. 4.181360202x + 4.370943285 + x2 = 1133501259000 + 4.370943285 Reorder the terms: 4.370943285 + 4.181360202x + x2 = 1133501259000 + 4.370943285 Combine like terms: 1133501259000 + 4.370943285 = 1133501259004.370943285 4.370943285 + 4.181360202x + x2 = 1133501259004.370943285 Factor a perfect square on the left side: (x + 2.090680101)(x + 2.090680101) = 1133501259004.370943285 Calculate the square root of the right side: 1064660.161274184 Break this problem into two subproblems by setting (x + 2.090680101) equal to 1064660.161274184 and -1064660.161274184.Subproblem 1
x + 2.090680101 = 1064660.161274184 Simplifying x + 2.090680101 = 1064660.161274184 Reorder the terms: 2.090680101 + x = 1064660.161274184 Solving 2.090680101 + x = 1064660.161274184 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.090680101' to each side of the equation. 2.090680101 + -2.090680101 + x = 1064660.161274184 + -2.090680101 Combine like terms: 2.090680101 + -2.090680101 = 0.000000000 0.000000000 + x = 1064660.161274184 + -2.090680101 x = 1064660.161274184 + -2.090680101 Combine like terms: 1064660.161274184 + -2.090680101 = 1064658.070594083 x = 1064658.070594083 Simplifying x = 1064658.070594083Subproblem 2
x + 2.090680101 = -1064660.161274184 Simplifying x + 2.090680101 = -1064660.161274184 Reorder the terms: 2.090680101 + x = -1064660.161274184 Solving 2.090680101 + x = -1064660.161274184 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.090680101' to each side of the equation. 2.090680101 + -2.090680101 + x = -1064660.161274184 + -2.090680101 Combine like terms: 2.090680101 + -2.090680101 = 0.000000000 0.000000000 + x = -1064660.161274184 + -2.090680101 x = -1064660.161274184 + -2.090680101 Combine like terms: -1064660.161274184 + -2.090680101 = -1064662.251954285 x = -1064662.251954285 Simplifying x = -1064662.251954285Solution
The solution to the problem is based on the solutions from the subproblems. x = {1064658.070594083, -1064662.251954285}
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