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Simplifying 1.5 + -20x + 50x2 = 0 Solving 1.5 + -20x + 50x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 50 the coefficient of the squared term: Divide each side by '50'. 0.03 + -0.4x + x2 = 0 Move the constant term to the right: Add '-0.03' to each side of the equation. 0.03 + -0.4x + -0.03 + x2 = 0 + -0.03 Reorder the terms: 0.03 + -0.03 + -0.4x + x2 = 0 + -0.03 Combine like terms: 0.03 + -0.03 = 0.00 0.00 + -0.4x + x2 = 0 + -0.03 -0.4x + x2 = 0 + -0.03 Combine like terms: 0 + -0.03 = -0.03 -0.4x + x2 = -0.03 The x term is -0.4x. Take half its coefficient (-0.2). Square it (0.04) and add it to both sides. Add '0.04' to each side of the equation. -0.4x + 0.04 + x2 = -0.03 + 0.04 Reorder the terms: 0.04 + -0.4x + x2 = -0.03 + 0.04 Combine like terms: -0.03 + 0.04 = 0.01 0.04 + -0.4x + x2 = 0.01 Factor a perfect square on the left side: (x + -0.2)(x + -0.2) = 0.01 Calculate the square root of the right side: 0.1 Break this problem into two subproblems by setting (x + -0.2) equal to 0.1 and -0.1.Subproblem 1
x + -0.2 = 0.1 Simplifying x + -0.2 = 0.1 Reorder the terms: -0.2 + x = 0.1 Solving -0.2 + x = 0.1 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2' to each side of the equation. -0.2 + 0.2 + x = 0.1 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + x = 0.1 + 0.2 x = 0.1 + 0.2 Combine like terms: 0.1 + 0.2 = 0.3 x = 0.3 Simplifying x = 0.3Subproblem 2
x + -0.2 = -0.1 Simplifying x + -0.2 = -0.1 Reorder the terms: -0.2 + x = -0.1 Solving -0.2 + x = -0.1 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2' to each side of the equation. -0.2 + 0.2 + x = -0.1 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + x = -0.1 + 0.2 x = -0.1 + 0.2 Combine like terms: -0.1 + 0.2 = 0.1 x = 0.1 Simplifying x = 0.1Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.3, 0.1}
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