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Simplifying x2 + -1.16x + 0.33 = 0 Reorder the terms: 0.33 + -1.16x + x2 = 0 Solving 0.33 + -1.16x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-0.33' to each side of the equation. 0.33 + -1.16x + -0.33 + x2 = 0 + -0.33 Reorder the terms: 0.33 + -0.33 + -1.16x + x2 = 0 + -0.33 Combine like terms: 0.33 + -0.33 = 0.00 0.00 + -1.16x + x2 = 0 + -0.33 -1.16x + x2 = 0 + -0.33 Combine like terms: 0 + -0.33 = -0.33 -1.16x + x2 = -0.33 The x term is -1.16x. Take half its coefficient (-0.58). Square it (0.3364) and add it to both sides. Add '0.3364' to each side of the equation. -1.16x + 0.3364 + x2 = -0.33 + 0.3364 Reorder the terms: 0.3364 + -1.16x + x2 = -0.33 + 0.3364 Combine like terms: -0.33 + 0.3364 = 0.0064 0.3364 + -1.16x + x2 = 0.0064 Factor a perfect square on the left side: (x + -0.58)(x + -0.58) = 0.0064 Calculate the square root of the right side: 0.08 Break this problem into two subproblems by setting (x + -0.58) equal to 0.08 and -0.08.Subproblem 1
x + -0.58 = 0.08 Simplifying x + -0.58 = 0.08 Reorder the terms: -0.58 + x = 0.08 Solving -0.58 + x = 0.08 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.58' to each side of the equation. -0.58 + 0.58 + x = 0.08 + 0.58 Combine like terms: -0.58 + 0.58 = 0.00 0.00 + x = 0.08 + 0.58 x = 0.08 + 0.58 Combine like terms: 0.08 + 0.58 = 0.66 x = 0.66 Simplifying x = 0.66Subproblem 2
x + -0.58 = -0.08 Simplifying x + -0.58 = -0.08 Reorder the terms: -0.58 + x = -0.08 Solving -0.58 + x = -0.08 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.58' to each side of the equation. -0.58 + 0.58 + x = -0.08 + 0.58 Combine like terms: -0.58 + 0.58 = 0.00 0.00 + x = -0.08 + 0.58 x = -0.08 + 0.58 Combine like terms: -0.08 + 0.58 = 0.5 x = 0.5 Simplifying x = 0.5Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.66, 0.5}
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