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Simplifying 10x2 + -17x + 2 = 0 Reorder the terms: 2 + -17x + 10x2 = 0 Solving 2 + -17x + 10x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. 0.2 + -1.7x + x2 = 0 Move the constant term to the right: Add '-0.2' to each side of the equation. 0.2 + -1.7x + -0.2 + x2 = 0 + -0.2 Reorder the terms: 0.2 + -0.2 + -1.7x + x2 = 0 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + -1.7x + x2 = 0 + -0.2 -1.7x + x2 = 0 + -0.2 Combine like terms: 0 + -0.2 = -0.2 -1.7x + x2 = -0.2 The x term is -1.7x. Take half its coefficient (-0.85). Square it (0.7225) and add it to both sides. Add '0.7225' to each side of the equation. -1.7x + 0.7225 + x2 = -0.2 + 0.7225 Reorder the terms: 0.7225 + -1.7x + x2 = -0.2 + 0.7225 Combine like terms: -0.2 + 0.7225 = 0.5225 0.7225 + -1.7x + x2 = 0.5225 Factor a perfect square on the left side: (x + -0.85)(x + -0.85) = 0.5225 Calculate the square root of the right side: 0.722841615 Break this problem into two subproblems by setting (x + -0.85) equal to 0.722841615 and -0.722841615.Subproblem 1
x + -0.85 = 0.722841615 Simplifying x + -0.85 = 0.722841615 Reorder the terms: -0.85 + x = 0.722841615 Solving -0.85 + x = 0.722841615 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.85' to each side of the equation. -0.85 + 0.85 + x = 0.722841615 + 0.85 Combine like terms: -0.85 + 0.85 = 0.00 0.00 + x = 0.722841615 + 0.85 x = 0.722841615 + 0.85 Combine like terms: 0.722841615 + 0.85 = 1.572841615 x = 1.572841615 Simplifying x = 1.572841615Subproblem 2
x + -0.85 = -0.722841615 Simplifying x + -0.85 = -0.722841615 Reorder the terms: -0.85 + x = -0.722841615 Solving -0.85 + x = -0.722841615 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.85' to each side of the equation. -0.85 + 0.85 + x = -0.722841615 + 0.85 Combine like terms: -0.85 + 0.85 = 0.00 0.00 + x = -0.722841615 + 0.85 x = -0.722841615 + 0.85 Combine like terms: -0.722841615 + 0.85 = 0.127158385 x = 0.127158385 Simplifying x = 0.127158385Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.572841615, 0.127158385}
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