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Simplifying 98.6x2 + -0.042025 + 4x = 0 Reorder the terms: -0.042025 + 4x + 98.6x2 = 0 Solving -0.042025 + 4x + 98.6x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 98.6 the coefficient of the squared term: Divide each side by '98.6'. -0.0004262170385 + 0.04056795132x + x2 = 0 Move the constant term to the right: Add '0.0004262170385' to each side of the equation. -0.0004262170385 + 0.04056795132x + 0.0004262170385 + x2 = 0 + 0.0004262170385 Reorder the terms: -0.0004262170385 + 0.0004262170385 + 0.04056795132x + x2 = 0 + 0.0004262170385 Combine like terms: -0.0004262170385 + 0.0004262170385 = 0.0000000000000 0.0000000000000 + 0.04056795132x + x2 = 0 + 0.0004262170385 0.04056795132x + x2 = 0 + 0.0004262170385 Combine like terms: 0 + 0.0004262170385 = 0.0004262170385 0.04056795132x + x2 = 0.0004262170385 The x term is 0.04056795132x. Take half its coefficient (0.02028397566). Square it (0.0004114396686) and add it to both sides. Add '0.0004114396686' to each side of the equation. 0.04056795132x + 0.0004114396686 + x2 = 0.0004262170385 + 0.0004114396686 Reorder the terms: 0.0004114396686 + 0.04056795132x + x2 = 0.0004262170385 + 0.0004114396686 Combine like terms: 0.0004262170385 + 0.0004114396686 = 0.0008376567071 0.0004114396686 + 0.04056795132x + x2 = 0.0008376567071 Factor a perfect square on the left side: (x + 0.02028397566)(x + 0.02028397566) = 0.0008376567071 Calculate the square root of the right side: 0.0289423 Break this problem into two subproblems by setting (x + 0.02028397566) equal to 0.0289423 and -0.0289423.Subproblem 1
x + 0.02028397566 = 0.0289423 Simplifying x + 0.02028397566 = 0.0289423 Reorder the terms: 0.02028397566 + x = 0.0289423 Solving 0.02028397566 + x = 0.0289423 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.02028397566' to each side of the equation. 0.02028397566 + -0.02028397566 + x = 0.0289423 + -0.02028397566 Combine like terms: 0.02028397566 + -0.02028397566 = 0.00000000000 0.00000000000 + x = 0.0289423 + -0.02028397566 x = 0.0289423 + -0.02028397566 Combine like terms: 0.0289423 + -0.02028397566 = 0.00865832434 x = 0.00865832434 Simplifying x = 0.00865832434Subproblem 2
x + 0.02028397566 = -0.0289423 Simplifying x + 0.02028397566 = -0.0289423 Reorder the terms: 0.02028397566 + x = -0.0289423 Solving 0.02028397566 + x = -0.0289423 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.02028397566' to each side of the equation. 0.02028397566 + -0.02028397566 + x = -0.0289423 + -0.02028397566 Combine like terms: 0.02028397566 + -0.02028397566 = 0.00000000000 0.00000000000 + x = -0.0289423 + -0.02028397566 x = -0.0289423 + -0.02028397566 Combine like terms: -0.0289423 + -0.02028397566 = -0.04922627566 x = -0.04922627566 Simplifying x = -0.04922627566Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.00865832434, -0.04922627566}
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