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Simplifying 1 + -0.75x + -0.3x2 = 0 Solving 1 + -0.75x + -0.3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.3 the coefficient of the squared term: Divide each side by '-0.3'. -3.333333333 + 2.5x + x2 = 0 Move the constant term to the right: Add '3.333333333' to each side of the equation. -3.333333333 + 2.5x + 3.333333333 + x2 = 0 + 3.333333333 Reorder the terms: -3.333333333 + 3.333333333 + 2.5x + x2 = 0 + 3.333333333 Combine like terms: -3.333333333 + 3.333333333 = 0.000000000 0.000000000 + 2.5x + x2 = 0 + 3.333333333 2.5x + x2 = 0 + 3.333333333 Combine like terms: 0 + 3.333333333 = 3.333333333 2.5x + x2 = 3.333333333 The x term is 2.5x. Take half its coefficient (1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. 2.5x + 1.5625 + x2 = 3.333333333 + 1.5625 Reorder the terms: 1.5625 + 2.5x + x2 = 3.333333333 + 1.5625 Combine like terms: 3.333333333 + 1.5625 = 4.895833333 1.5625 + 2.5x + x2 = 4.895833333 Factor a perfect square on the left side: (x + 1.25)(x + 1.25) = 4.895833333 Calculate the square root of the right side: 2.212653008 Break this problem into two subproblems by setting (x + 1.25) equal to 2.212653008 and -2.212653008.Subproblem 1
x + 1.25 = 2.212653008 Simplifying x + 1.25 = 2.212653008 Reorder the terms: 1.25 + x = 2.212653008 Solving 1.25 + x = 2.212653008 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = 2.212653008 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = 2.212653008 + -1.25 x = 2.212653008 + -1.25 Combine like terms: 2.212653008 + -1.25 = 0.962653008 x = 0.962653008 Simplifying x = 0.962653008Subproblem 2
x + 1.25 = -2.212653008 Simplifying x + 1.25 = -2.212653008 Reorder the terms: 1.25 + x = -2.212653008 Solving 1.25 + x = -2.212653008 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = -2.212653008 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = -2.212653008 + -1.25 x = -2.212653008 + -1.25 Combine like terms: -2.212653008 + -1.25 = -3.462653008 x = -3.462653008 Simplifying x = -3.462653008Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.962653008, -3.462653008}
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