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Simplifying x2 + -1.7x + 0.6 = 0 Reorder the terms: 0.6 + -1.7x + x2 = 0 Solving 0.6 + -1.7x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-0.6' to each side of the equation. 0.6 + -1.7x + -0.6 + x2 = 0 + -0.6 Reorder the terms: 0.6 + -0.6 + -1.7x + x2 = 0 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + -1.7x + x2 = 0 + -0.6 -1.7x + x2 = 0 + -0.6 Combine like terms: 0 + -0.6 = -0.6 -1.7x + x2 = -0.6 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 = -0.6 + 0.7225 Reorder the terms: 0.7225 + -1.7x + x2 = -0.6 + 0.7225 Combine like terms: -0.6 + 0.7225 = 0.1225 0.7225 + -1.7x + x2 = 0.1225 Factor a perfect square on the left side: (x + -0.85)(x + -0.85) = 0.1225 Calculate the square root of the right side: 0.35 Break this problem into two subproblems by setting (x + -0.85) equal to 0.35 and -0.35.Subproblem 1
x + -0.85 = 0.35 Simplifying x + -0.85 = 0.35 Reorder the terms: -0.85 + x = 0.35 Solving -0.85 + x = 0.35 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 = 0.35 + 0.85 Combine like terms: -0.85 + 0.85 = 0.00 0.00 + x = 0.35 + 0.85 x = 0.35 + 0.85 Combine like terms: 0.35 + 0.85 = 1.2 x = 1.2 Simplifying x = 1.2Subproblem 2
x + -0.85 = -0.35 Simplifying x + -0.85 = -0.35 Reorder the terms: -0.85 + x = -0.35 Solving -0.85 + x = -0.35 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 = -0.35 + 0.85 Combine like terms: -0.85 + 0.85 = 0.00 0.00 + x = -0.35 + 0.85 x = -0.35 + 0.85 Combine like terms: -0.35 + 0.85 = 0.5 x = 0.5 Simplifying x = 0.5Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.2, 0.5}
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