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Simplifying 1 + -11x + 5x2 = 0 Solving 1 + -11x + 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'. 0.2 + -2.2x + x2 = 0 Move the constant term to the right: Add '-0.2' to each side of the equation. 0.2 + -2.2x + -0.2 + x2 = 0 + -0.2 Reorder the terms: 0.2 + -0.2 + -2.2x + x2 = 0 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + -2.2x + x2 = 0 + -0.2 -2.2x + x2 = 0 + -0.2 Combine like terms: 0 + -0.2 = -0.2 -2.2x + x2 = -0.2 The x term is -2.2x. Take half its coefficient (-1.1). Square it (1.21) and add it to both sides. Add '1.21' to each side of the equation. -2.2x + 1.21 + x2 = -0.2 + 1.21 Reorder the terms: 1.21 + -2.2x + x2 = -0.2 + 1.21 Combine like terms: -0.2 + 1.21 = 1.01 1.21 + -2.2x + x2 = 1.01 Factor a perfect square on the left side: (x + -1.1)(x + -1.1) = 1.01 Calculate the square root of the right side: 1.004987562 Break this problem into two subproblems by setting (x + -1.1) equal to 1.004987562 and -1.004987562.Subproblem 1
x + -1.1 = 1.004987562 Simplifying x + -1.1 = 1.004987562 Reorder the terms: -1.1 + x = 1.004987562 Solving -1.1 + x = 1.004987562 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.1' to each side of the equation. -1.1 + 1.1 + x = 1.004987562 + 1.1 Combine like terms: -1.1 + 1.1 = 0.0 0.0 + x = 1.004987562 + 1.1 x = 1.004987562 + 1.1 Combine like terms: 1.004987562 + 1.1 = 2.104987562 x = 2.104987562 Simplifying x = 2.104987562Subproblem 2
x + -1.1 = -1.004987562 Simplifying x + -1.1 = -1.004987562 Reorder the terms: -1.1 + x = -1.004987562 Solving -1.1 + x = -1.004987562 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.1' to each side of the equation. -1.1 + 1.1 + x = -1.004987562 + 1.1 Combine like terms: -1.1 + 1.1 = 0.0 0.0 + x = -1.004987562 + 1.1 x = -1.004987562 + 1.1 Combine like terms: -1.004987562 + 1.1 = 0.095012438 x = 0.095012438 Simplifying x = 0.095012438Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.104987562, 0.095012438}
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