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Simplifying 2x2 + -3x + -196 = 0 Reorder the terms: -196 + -3x + 2x2 = 0 Solving -196 + -3x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -98 + -1.5x + x2 = 0 Move the constant term to the right: Add '98' to each side of the equation. -98 + -1.5x + 98 + x2 = 0 + 98 Reorder the terms: -98 + 98 + -1.5x + x2 = 0 + 98 Combine like terms: -98 + 98 = 0 0 + -1.5x + x2 = 0 + 98 -1.5x + x2 = 0 + 98 Combine like terms: 0 + 98 = 98 -1.5x + x2 = 98 The x term is -1.5x. Take half its coefficient (-0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. -1.5x + 0.5625 + x2 = 98 + 0.5625 Reorder the terms: 0.5625 + -1.5x + x2 = 98 + 0.5625 Combine like terms: 98 + 0.5625 = 98.5625 0.5625 + -1.5x + x2 = 98.5625 Factor a perfect square on the left side: (x + -0.75)(x + -0.75) = 98.5625 Calculate the square root of the right side: 9.927864826 Break this problem into two subproblems by setting (x + -0.75) equal to 9.927864826 and -9.927864826.Subproblem 1
x + -0.75 = 9.927864826 Simplifying x + -0.75 = 9.927864826 Reorder the terms: -0.75 + x = 9.927864826 Solving -0.75 + x = 9.927864826 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = 9.927864826 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = 9.927864826 + 0.75 x = 9.927864826 + 0.75 Combine like terms: 9.927864826 + 0.75 = 10.677864826 x = 10.677864826 Simplifying x = 10.677864826Subproblem 2
x + -0.75 = -9.927864826 Simplifying x + -0.75 = -9.927864826 Reorder the terms: -0.75 + x = -9.927864826 Solving -0.75 + x = -9.927864826 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = -9.927864826 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = -9.927864826 + 0.75 x = -9.927864826 + 0.75 Combine like terms: -9.927864826 + 0.75 = -9.177864826 x = -9.177864826 Simplifying x = -9.177864826Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.677864826, -9.177864826}
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