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Simplifying 4.9x2 + 3x + -1.9 = 0 Reorder the terms: -1.9 + 3x + 4.9x2 = 0 Solving -1.9 + 3x + 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'. -0.387755102 + 0.612244898x + x2 = 0 Move the constant term to the right: Add '0.387755102' to each side of the equation. -0.387755102 + 0.612244898x + 0.387755102 + x2 = 0 + 0.387755102 Reorder the terms: -0.387755102 + 0.387755102 + 0.612244898x + x2 = 0 + 0.387755102 Combine like terms: -0.387755102 + 0.387755102 = 0.000000000 0.000000000 + 0.612244898x + x2 = 0 + 0.387755102 0.612244898x + x2 = 0 + 0.387755102 Combine like terms: 0 + 0.387755102 = 0.387755102 0.612244898x + x2 = 0.387755102 The x term is 0.612244898x. Take half its coefficient (0.306122449). Square it (0.09371095378) and add it to both sides. Add '0.09371095378' to each side of the equation. 0.612244898x + 0.09371095378 + x2 = 0.387755102 + 0.09371095378 Reorder the terms: 0.09371095378 + 0.612244898x + x2 = 0.387755102 + 0.09371095378 Combine like terms: 0.387755102 + 0.09371095378 = 0.48146605578 0.09371095378 + 0.612244898x + x2 = 0.48146605578 Factor a perfect square on the left side: (x + 0.306122449)(x + 0.306122449) = 0.48146605578 Calculate the square root of the right side: 0.693877551 Break this problem into two subproblems by setting (x + 0.306122449) equal to 0.693877551 and -0.693877551.Subproblem 1
x + 0.306122449 = 0.693877551 Simplifying x + 0.306122449 = 0.693877551 Reorder the terms: 0.306122449 + x = 0.693877551 Solving 0.306122449 + x = 0.693877551 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.306122449' to each side of the equation. 0.306122449 + -0.306122449 + x = 0.693877551 + -0.306122449 Combine like terms: 0.306122449 + -0.306122449 = 0.000000000 0.000000000 + x = 0.693877551 + -0.306122449 x = 0.693877551 + -0.306122449 Combine like terms: 0.693877551 + -0.306122449 = 0.387755102 x = 0.387755102 Simplifying x = 0.387755102Subproblem 2
x + 0.306122449 = -0.693877551 Simplifying x + 0.306122449 = -0.693877551 Reorder the terms: 0.306122449 + x = -0.693877551 Solving 0.306122449 + x = -0.693877551 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.306122449' to each side of the equation. 0.306122449 + -0.306122449 + x = -0.693877551 + -0.306122449 Combine like terms: 0.306122449 + -0.306122449 = 0.000000000 0.000000000 + x = -0.693877551 + -0.306122449 x = -0.693877551 + -0.306122449 Combine like terms: -0.693877551 + -0.306122449 = -1 x = -1 Simplifying x = -1Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.387755102, -1}
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