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Simplifying 2x2 + -3x + 0.05 = 0 Reorder the terms: 0.05 + -3x + 2x2 = 0 Solving 0.05 + -3x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 0.025 + -1.5x + x2 = 0 Move the constant term to the right: Add '-0.025' to each side of the equation. 0.025 + -1.5x + -0.025 + x2 = 0 + -0.025 Reorder the terms: 0.025 + -0.025 + -1.5x + x2 = 0 + -0.025 Combine like terms: 0.025 + -0.025 = 0.000 0.000 + -1.5x + x2 = 0 + -0.025 -1.5x + x2 = 0 + -0.025 Combine like terms: 0 + -0.025 = -0.025 -1.5x + x2 = -0.025 The x term is -1.5x. Take half its coefficient (-0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. -1.5x + 0.5625 + x2 = -0.025 + 0.5625 Reorder the terms: 0.5625 + -1.5x + x2 = -0.025 + 0.5625 Combine like terms: -0.025 + 0.5625 = 0.5375 0.5625 + -1.5x + x2 = 0.5375 Factor a perfect square on the left side: (x + -0.75)(x + -0.75) = 0.5375 Calculate the square root of the right side: 0.733143915 Break this problem into two subproblems by setting (x + -0.75) equal to 0.733143915 and -0.733143915.Subproblem 1
x + -0.75 = 0.733143915 Simplifying x + -0.75 = 0.733143915 Reorder the terms: -0.75 + x = 0.733143915 Solving -0.75 + x = 0.733143915 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = 0.733143915 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = 0.733143915 + 0.75 x = 0.733143915 + 0.75 Combine like terms: 0.733143915 + 0.75 = 1.483143915 x = 1.483143915 Simplifying x = 1.483143915Subproblem 2
x + -0.75 = -0.733143915 Simplifying x + -0.75 = -0.733143915 Reorder the terms: -0.75 + x = -0.733143915 Solving -0.75 + x = -0.733143915 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = -0.733143915 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = -0.733143915 + 0.75 x = -0.733143915 + 0.75 Combine like terms: -0.733143915 + 0.75 = 0.016856085 x = 0.016856085 Simplifying x = 0.016856085Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.483143915, 0.016856085}
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