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Simplifying 1 + -0.6x + 0.08x2 = 0 Solving 1 + -0.6x + 0.08x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.08 the coefficient of the squared term: Divide each side by '0.08'. 12.5 + -7.5x + x2 = 0 Move the constant term to the right: Add '-12.5' to each side of the equation. 12.5 + -7.5x + -12.5 + x2 = 0 + -12.5 Reorder the terms: 12.5 + -12.5 + -7.5x + x2 = 0 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + -7.5x + x2 = 0 + -12.5 -7.5x + x2 = 0 + -12.5 Combine like terms: 0 + -12.5 = -12.5 -7.5x + x2 = -12.5 The x term is -7.5x. Take half its coefficient (-3.75). Square it (14.0625) and add it to both sides. Add '14.0625' to each side of the equation. -7.5x + 14.0625 + x2 = -12.5 + 14.0625 Reorder the terms: 14.0625 + -7.5x + x2 = -12.5 + 14.0625 Combine like terms: -12.5 + 14.0625 = 1.5625 14.0625 + -7.5x + x2 = 1.5625 Factor a perfect square on the left side: (x + -3.75)(x + -3.75) = 1.5625 Calculate the square root of the right side: 1.25 Break this problem into two subproblems by setting (x + -3.75) equal to 1.25 and -1.25.Subproblem 1
x + -3.75 = 1.25 Simplifying x + -3.75 = 1.25 Reorder the terms: -3.75 + x = 1.25 Solving -3.75 + x = 1.25 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.75' to each side of the equation. -3.75 + 3.75 + x = 1.25 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + x = 1.25 + 3.75 x = 1.25 + 3.75 Combine like terms: 1.25 + 3.75 = 5 x = 5 Simplifying x = 5Subproblem 2
x + -3.75 = -1.25 Simplifying x + -3.75 = -1.25 Reorder the terms: -3.75 + x = -1.25 Solving -3.75 + x = -1.25 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.75' to each side of the equation. -3.75 + 3.75 + x = -1.25 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + x = -1.25 + 3.75 x = -1.25 + 3.75 Combine like terms: -1.25 + 3.75 = 2.5 x = 2.5 Simplifying x = 2.5Solution
The solution to the problem is based on the solutions from the subproblems. x = {5, 2.5}
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