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Simplifying 0.125x2 + -1.625x + 5 = 0 Reorder the terms: 5 + -1.625x + 0.125x2 = 0 Solving 5 + -1.625x + 0.125x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.125 the coefficient of the squared term: Divide each side by '0.125'. 40 + -13x + x2 = 0 Move the constant term to the right: Add '-40' to each side of the equation. 40 + -13x + -40 + x2 = 0 + -40 Reorder the terms: 40 + -40 + -13x + x2 = 0 + -40 Combine like terms: 40 + -40 = 0 0 + -13x + x2 = 0 + -40 -13x + x2 = 0 + -40 Combine like terms: 0 + -40 = -40 -13x + x2 = -40 The x term is -13x. Take half its coefficient (-6.5). Square it (42.25) and add it to both sides. Add '42.25' to each side of the equation. -13x + 42.25 + x2 = -40 + 42.25 Reorder the terms: 42.25 + -13x + x2 = -40 + 42.25 Combine like terms: -40 + 42.25 = 2.25 42.25 + -13x + x2 = 2.25 Factor a perfect square on the left side: (x + -6.5)(x + -6.5) = 2.25 Calculate the square root of the right side: 1.5 Break this problem into two subproblems by setting (x + -6.5) equal to 1.5 and -1.5.Subproblem 1
x + -6.5 = 1.5 Simplifying x + -6.5 = 1.5 Reorder the terms: -6.5 + x = 1.5 Solving -6.5 + x = 1.5 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + x = 1.5 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + x = 1.5 + 6.5 x = 1.5 + 6.5 Combine like terms: 1.5 + 6.5 = 8 x = 8 Simplifying x = 8Subproblem 2
x + -6.5 = -1.5 Simplifying x + -6.5 = -1.5 Reorder the terms: -6.5 + x = -1.5 Solving -6.5 + x = -1.5 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + x = -1.5 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + x = -1.5 + 6.5 x = -1.5 + 6.5 Combine like terms: -1.5 + 6.5 = 5 x = 5 Simplifying x = 5Solution
The solution to the problem is based on the solutions from the subproblems. x = {8, 5}
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