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Simplifying x2 + -1.7x + 0.72 = 0 Reorder the terms: 0.72 + -1.7x + x2 = 0 Solving 0.72 + -1.7x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-0.72' to each side of the equation. 0.72 + -1.7x + -0.72 + x2 = 0 + -0.72 Reorder the terms: 0.72 + -0.72 + -1.7x + x2 = 0 + -0.72 Combine like terms: 0.72 + -0.72 = 0.00 0.00 + -1.7x + x2 = 0 + -0.72 -1.7x + x2 = 0 + -0.72 Combine like terms: 0 + -0.72 = -0.72 -1.7x + x2 = -0.72 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 = -0.72 + 0.7225 Reorder the terms: 0.7225 + -1.7x + x2 = -0.72 + 0.7225 Combine like terms: -0.72 + 0.7225 = 0.0025 0.7225 + -1.7x + x2 = 0.0025 Factor a perfect square on the left side: (x + -0.85)(x + -0.85) = 0.0025 Calculate the square root of the right side: 0.05 Break this problem into two subproblems by setting (x + -0.85) equal to 0.05 and -0.05.Subproblem 1
x + -0.85 = 0.05 Simplifying x + -0.85 = 0.05 Reorder the terms: -0.85 + x = 0.05 Solving -0.85 + x = 0.05 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 = 0.05 + 0.85 Combine like terms: -0.85 + 0.85 = 0.00 0.00 + x = 0.05 + 0.85 x = 0.05 + 0.85 Combine like terms: 0.05 + 0.85 = 0.9 x = 0.9 Simplifying x = 0.9Subproblem 2
x + -0.85 = -0.05 Simplifying x + -0.85 = -0.05 Reorder the terms: -0.85 + x = -0.05 Solving -0.85 + x = -0.05 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 = -0.05 + 0.85 Combine like terms: -0.85 + 0.85 = 0.00 0.00 + x = -0.05 + 0.85 x = -0.05 + 0.85 Combine like terms: -0.05 + 0.85 = 0.8 x = 0.8 Simplifying x = 0.8Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.9, 0.8}
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