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Simplifying 0.87x2 + -2x + 0.87 = 0 Reorder the terms: 0.87 + -2x + 0.87x2 = 0 Solving 0.87 + -2x + 0.87x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.87 the coefficient of the squared term: Divide each side by '0.87'. 1 + -2.298850575x + x2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + -2.298850575x + -1 + x2 = 0 + -1 Reorder the terms: 1 + -1 + -2.298850575x + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2.298850575x + x2 = 0 + -1 -2.298850575x + x2 = 0 + -1 Combine like terms: 0 + -1 = -1 -2.298850575x + x2 = -1 The x term is -2.298850575x. Take half its coefficient (-1.149425288). Square it (1.321178493) and add it to both sides. Add '1.321178493' to each side of the equation. -2.298850575x + 1.321178493 + x2 = -1 + 1.321178493 Reorder the terms: 1.321178493 + -2.298850575x + x2 = -1 + 1.321178493 Combine like terms: -1 + 1.321178493 = 0.321178493 1.321178493 + -2.298850575x + x2 = 0.321178493 Factor a perfect square on the left side: (x + -1.149425288)(x + -1.149425288) = 0.321178493 Calculate the square root of the right side: 0.566726118 Break this problem into two subproblems by setting (x + -1.149425288) equal to 0.566726118 and -0.566726118.Subproblem 1
x + -1.149425288 = 0.566726118 Simplifying x + -1.149425288 = 0.566726118 Reorder the terms: -1.149425288 + x = 0.566726118 Solving -1.149425288 + x = 0.566726118 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.149425288' to each side of the equation. -1.149425288 + 1.149425288 + x = 0.566726118 + 1.149425288 Combine like terms: -1.149425288 + 1.149425288 = 0.000000000 0.000000000 + x = 0.566726118 + 1.149425288 x = 0.566726118 + 1.149425288 Combine like terms: 0.566726118 + 1.149425288 = 1.716151406 x = 1.716151406 Simplifying x = 1.716151406Subproblem 2
x + -1.149425288 = -0.566726118 Simplifying x + -1.149425288 = -0.566726118 Reorder the terms: -1.149425288 + x = -0.566726118 Solving -1.149425288 + x = -0.566726118 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.149425288' to each side of the equation. -1.149425288 + 1.149425288 + x = -0.566726118 + 1.149425288 Combine like terms: -1.149425288 + 1.149425288 = 0.000000000 0.000000000 + x = -0.566726118 + 1.149425288 x = -0.566726118 + 1.149425288 Combine like terms: -0.566726118 + 1.149425288 = 0.58269917 x = 0.58269917 Simplifying x = 0.58269917Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.716151406, 0.58269917}
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