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Simplifying 0.25x2 + -0.04x + -0.024 = 0 Reorder the terms: -0.024 + -0.04x + 0.25x2 = 0 Solving -0.024 + -0.04x + 0.25x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.25 the coefficient of the squared term: Divide each side by '0.25'. -0.096 + -0.16x + x2 = 0 Move the constant term to the right: Add '0.096' to each side of the equation. -0.096 + -0.16x + 0.096 + x2 = 0 + 0.096 Reorder the terms: -0.096 + 0.096 + -0.16x + x2 = 0 + 0.096 Combine like terms: -0.096 + 0.096 = 0.000 0.000 + -0.16x + x2 = 0 + 0.096 -0.16x + x2 = 0 + 0.096 Combine like terms: 0 + 0.096 = 0.096 -0.16x + x2 = 0.096 The x term is -0.16x. Take half its coefficient (-0.08). Square it (0.0064) and add it to both sides. Add '0.0064' to each side of the equation. -0.16x + 0.0064 + x2 = 0.096 + 0.0064 Reorder the terms: 0.0064 + -0.16x + x2 = 0.096 + 0.0064 Combine like terms: 0.096 + 0.0064 = 0.1024 0.0064 + -0.16x + x2 = 0.1024 Factor a perfect square on the left side: (x + -0.08)(x + -0.08) = 0.1024 Calculate the square root of the right side: 0.32 Break this problem into two subproblems by setting (x + -0.08) equal to 0.32 and -0.32.Subproblem 1
x + -0.08 = 0.32 Simplifying x + -0.08 = 0.32 Reorder the terms: -0.08 + x = 0.32 Solving -0.08 + x = 0.32 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.08' to each side of the equation. -0.08 + 0.08 + x = 0.32 + 0.08 Combine like terms: -0.08 + 0.08 = 0.00 0.00 + x = 0.32 + 0.08 x = 0.32 + 0.08 Combine like terms: 0.32 + 0.08 = 0.4 x = 0.4 Simplifying x = 0.4Subproblem 2
x + -0.08 = -0.32 Simplifying x + -0.08 = -0.32 Reorder the terms: -0.08 + x = -0.32 Solving -0.08 + x = -0.32 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.08' to each side of the equation. -0.08 + 0.08 + x = -0.32 + 0.08 Combine like terms: -0.08 + 0.08 = 0.00 0.00 + x = -0.32 + 0.08 x = -0.32 + 0.08 Combine like terms: -0.32 + 0.08 = -0.24 x = -0.24 Simplifying x = -0.24Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.4, -0.24}
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