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Simplifying 98x2 + 291x + -130 = 0 Reorder the terms: -130 + 291x + 98x2 = 0 Solving -130 + 291x + 98x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 98 the coefficient of the squared term: Divide each side by '98'. -1.326530612 + 2.969387755x + x2 = 0 Move the constant term to the right: Add '1.326530612' to each side of the equation. -1.326530612 + 2.969387755x + 1.326530612 + x2 = 0 + 1.326530612 Reorder the terms: -1.326530612 + 1.326530612 + 2.969387755x + x2 = 0 + 1.326530612 Combine like terms: -1.326530612 + 1.326530612 = 0.000000000 0.000000000 + 2.969387755x + x2 = 0 + 1.326530612 2.969387755x + x2 = 0 + 1.326530612 Combine like terms: 0 + 1.326530612 = 1.326530612 2.969387755x + x2 = 1.326530612 The x term is 2.969387755x. Take half its coefficient (1.484693878). Square it (2.204315911) and add it to both sides. Add '2.204315911' to each side of the equation. 2.969387755x + 2.204315911 + x2 = 1.326530612 + 2.204315911 Reorder the terms: 2.204315911 + 2.969387755x + x2 = 1.326530612 + 2.204315911 Combine like terms: 1.326530612 + 2.204315911 = 3.530846523 2.204315911 + 2.969387755x + x2 = 3.530846523 Factor a perfect square on the left side: (x + 1.484693878)(x + 1.484693878) = 3.530846523 Calculate the square root of the right side: 1.879054689 Break this problem into two subproblems by setting (x + 1.484693878) equal to 1.879054689 and -1.879054689.Subproblem 1
x + 1.484693878 = 1.879054689 Simplifying x + 1.484693878 = 1.879054689 Reorder the terms: 1.484693878 + x = 1.879054689 Solving 1.484693878 + x = 1.879054689 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.484693878' to each side of the equation. 1.484693878 + -1.484693878 + x = 1.879054689 + -1.484693878 Combine like terms: 1.484693878 + -1.484693878 = 0.000000000 0.000000000 + x = 1.879054689 + -1.484693878 x = 1.879054689 + -1.484693878 Combine like terms: 1.879054689 + -1.484693878 = 0.394360811 x = 0.394360811 Simplifying x = 0.394360811Subproblem 2
x + 1.484693878 = -1.879054689 Simplifying x + 1.484693878 = -1.879054689 Reorder the terms: 1.484693878 + x = -1.879054689 Solving 1.484693878 + x = -1.879054689 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.484693878' to each side of the equation. 1.484693878 + -1.484693878 + x = -1.879054689 + -1.484693878 Combine like terms: 1.484693878 + -1.484693878 = 0.000000000 0.000000000 + x = -1.879054689 + -1.484693878 x = -1.879054689 + -1.484693878 Combine like terms: -1.879054689 + -1.484693878 = -3.363748567 x = -3.363748567 Simplifying x = -3.363748567Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.394360811, -3.363748567}
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