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Simplifying -5x2 + 14.1x + 5 = 0 Reorder the terms: 5 + 14.1x + -5x2 = 0 Solving 5 + 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 + -2.82x + x2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + -2.82x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + -2.82x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -2.82x + x2 = 0 + 1 -2.82x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 -2.82x + x2 = 1 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 + 1.9881 Reorder the terms: 1.9881 + -2.82x + x2 = 1 + 1.9881 Combine like terms: 1 + 1.9881 = 2.9881 1.9881 + -2.82x + x2 = 2.9881 Factor a perfect square on the left side: (x + -1.41)(x + -1.41) = 2.9881 Calculate the square root of the right side: 1.72861216 Break this problem into two subproblems by setting (x + -1.41) equal to 1.72861216 and -1.72861216.Subproblem 1
x + -1.41 = 1.72861216 Simplifying x + -1.41 = 1.72861216 Reorder the terms: -1.41 + x = 1.72861216 Solving -1.41 + x = 1.72861216 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 = 1.72861216 + 1.41 Combine like terms: -1.41 + 1.41 = 0.00 0.00 + x = 1.72861216 + 1.41 x = 1.72861216 + 1.41 Combine like terms: 1.72861216 + 1.41 = 3.13861216 x = 3.13861216 Simplifying x = 3.13861216Subproblem 2
x + -1.41 = -1.72861216 Simplifying x + -1.41 = -1.72861216 Reorder the terms: -1.41 + x = -1.72861216 Solving -1.41 + x = -1.72861216 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 = -1.72861216 + 1.41 Combine like terms: -1.41 + 1.41 = 0.00 0.00 + x = -1.72861216 + 1.41 x = -1.72861216 + 1.41 Combine like terms: -1.72861216 + 1.41 = -0.31861216 x = -0.31861216 Simplifying x = -0.31861216Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.13861216, -0.31861216}
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