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Simplifying -5x2 + 14.1x + -9 = 0 Reorder the terms: -9 + 14.1x + -5x2 = 0 Solving -9 + 14.1x + -5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. 1.8 + -2.82x + x2 = 0 Move the constant term to the right: Add '-1.8' to each side of the equation. 1.8 + -2.82x + -1.8 + x2 = 0 + -1.8 Reorder the terms: 1.8 + -1.8 + -2.82x + x2 = 0 + -1.8 Combine like terms: 1.8 + -1.8 = 0.0 0.0 + -2.82x + x2 = 0 + -1.8 -2.82x + x2 = 0 + -1.8 Combine like terms: 0 + -1.8 = -1.8 -2.82x + x2 = -1.8 The x term is -2.82x. Take half its coefficient (-1.41). Square it (1.9881) and add it to both sides. Add '1.9881' to each side of the equation. -2.82x + 1.9881 + x2 = -1.8 + 1.9881 Reorder the terms: 1.9881 + -2.82x + x2 = -1.8 + 1.9881 Combine like terms: -1.8 + 1.9881 = 0.1881 1.9881 + -2.82x + x2 = 0.1881 Factor a perfect square on the left side: (x + -1.41)(x + -1.41) = 0.1881 Calculate the square root of the right side: 0.433704969 Break this problem into two subproblems by setting (x + -1.41) equal to 0.433704969 and -0.433704969.Subproblem 1
x + -1.41 = 0.433704969 Simplifying x + -1.41 = 0.433704969 Reorder the terms: -1.41 + x = 0.433704969 Solving -1.41 + x = 0.433704969 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.41' to each side of the equation. -1.41 + 1.41 + x = 0.433704969 + 1.41 Combine like terms: -1.41 + 1.41 = 0.00 0.00 + x = 0.433704969 + 1.41 x = 0.433704969 + 1.41 Combine like terms: 0.433704969 + 1.41 = 1.843704969 x = 1.843704969 Simplifying x = 1.843704969Subproblem 2
x + -1.41 = -0.433704969 Simplifying x + -1.41 = -0.433704969 Reorder the terms: -1.41 + x = -0.433704969 Solving -1.41 + x = -0.433704969 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.41' to each side of the equation. -1.41 + 1.41 + x = -0.433704969 + 1.41 Combine like terms: -1.41 + 1.41 = 0.00 0.00 + x = -0.433704969 + 1.41 x = -0.433704969 + 1.41 Combine like terms: -0.433704969 + 1.41 = 0.976295031 x = 0.976295031 Simplifying x = 0.976295031Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.843704969, 0.976295031}
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