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Simplifying -4.90x2 + 12.4x + 2.50 = 0 Reorder the terms: 2.50 + 12.4x + -4.90x2 = 0 Solving 2.50 + 12.4x + -4.90x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -4.90 the coefficient of the squared term: Divide each side by '-4.90'. -0.5102040816 + -2.530612245x + x2 = 0 Move the constant term to the right: Add '0.5102040816' to each side of the equation. -0.5102040816 + -2.530612245x + 0.5102040816 + x2 = 0 + 0.5102040816 Reorder the terms: -0.5102040816 + 0.5102040816 + -2.530612245x + x2 = 0 + 0.5102040816 Combine like terms: -0.5102040816 + 0.5102040816 = 0.0000000000 0.0000000000 + -2.530612245x + x2 = 0 + 0.5102040816 -2.530612245x + x2 = 0 + 0.5102040816 Combine like terms: 0 + 0.5102040816 = 0.5102040816 -2.530612245x + x2 = 0.5102040816 The x term is -2.530612245x. Take half its coefficient (-1.265306123). Square it (1.600999585) and add it to both sides. Add '1.600999585' to each side of the equation. -2.530612245x + 1.600999585 + x2 = 0.5102040816 + 1.600999585 Reorder the terms: 1.600999585 + -2.530612245x + x2 = 0.5102040816 + 1.600999585 Combine like terms: 0.5102040816 + 1.600999585 = 2.1112036666 1.600999585 + -2.530612245x + x2 = 2.1112036666 Factor a perfect square on the left side: (x + -1.265306123)(x + -1.265306123) = 2.1112036666 Calculate the square root of the right side: 1.452998165 Break this problem into two subproblems by setting (x + -1.265306123) equal to 1.452998165 and -1.452998165.Subproblem 1
x + -1.265306123 = 1.452998165 Simplifying x + -1.265306123 = 1.452998165 Reorder the terms: -1.265306123 + x = 1.452998165 Solving -1.265306123 + x = 1.452998165 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.265306123' to each side of the equation. -1.265306123 + 1.265306123 + x = 1.452998165 + 1.265306123 Combine like terms: -1.265306123 + 1.265306123 = 0.000000000 0.000000000 + x = 1.452998165 + 1.265306123 x = 1.452998165 + 1.265306123 Combine like terms: 1.452998165 + 1.265306123 = 2.718304288 x = 2.718304288 Simplifying x = 2.718304288Subproblem 2
x + -1.265306123 = -1.452998165 Simplifying x + -1.265306123 = -1.452998165 Reorder the terms: -1.265306123 + x = -1.452998165 Solving -1.265306123 + x = -1.452998165 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.265306123' to each side of the equation. -1.265306123 + 1.265306123 + x = -1.452998165 + 1.265306123 Combine like terms: -1.265306123 + 1.265306123 = 0.000000000 0.000000000 + x = -1.452998165 + 1.265306123 x = -1.452998165 + 1.265306123 Combine like terms: -1.452998165 + 1.265306123 = -0.187692042 x = -0.187692042 Simplifying x = -0.187692042Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.718304288, -0.187692042}
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