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Simplifying 1.4x2 + -2.5x + -1 = 0 Reorder the terms: -1 + -2.5x + 1.4x2 = 0 Solving -1 + -2.5x + 1.4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 1.4 the coefficient of the squared term: Divide each side by '1.4'. -0.7142857143 + -1.785714286x + x2 = 0 Move the constant term to the right: Add '0.7142857143' to each side of the equation. -0.7142857143 + -1.785714286x + 0.7142857143 + x2 = 0 + 0.7142857143 Reorder the terms: -0.7142857143 + 0.7142857143 + -1.785714286x + x2 = 0 + 0.7142857143 Combine like terms: -0.7142857143 + 0.7142857143 = 0.0000000000 0.0000000000 + -1.785714286x + x2 = 0 + 0.7142857143 -1.785714286x + x2 = 0 + 0.7142857143 Combine like terms: 0 + 0.7142857143 = 0.7142857143 -1.785714286x + x2 = 0.7142857143 The x term is -1.785714286x. Take half its coefficient (-0.892857143). Square it (0.7971938778) and add it to both sides. Add '0.7971938778' to each side of the equation. -1.785714286x + 0.7971938778 + x2 = 0.7142857143 + 0.7971938778 Reorder the terms: 0.7971938778 + -1.785714286x + x2 = 0.7142857143 + 0.7971938778 Combine like terms: 0.7142857143 + 0.7971938778 = 1.5114795921 0.7971938778 + -1.785714286x + x2 = 1.5114795921 Factor a perfect square on the left side: (x + -0.892857143)(x + -0.892857143) = 1.5114795921 Calculate the square root of the right side: 1.229422463 Break this problem into two subproblems by setting (x + -0.892857143) equal to 1.229422463 and -1.229422463.Subproblem 1
x + -0.892857143 = 1.229422463 Simplifying x + -0.892857143 = 1.229422463 Reorder the terms: -0.892857143 + x = 1.229422463 Solving -0.892857143 + x = 1.229422463 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.892857143' to each side of the equation. -0.892857143 + 0.892857143 + x = 1.229422463 + 0.892857143 Combine like terms: -0.892857143 + 0.892857143 = 0.000000000 0.000000000 + x = 1.229422463 + 0.892857143 x = 1.229422463 + 0.892857143 Combine like terms: 1.229422463 + 0.892857143 = 2.122279606 x = 2.122279606 Simplifying x = 2.122279606Subproblem 2
x + -0.892857143 = -1.229422463 Simplifying x + -0.892857143 = -1.229422463 Reorder the terms: -0.892857143 + x = -1.229422463 Solving -0.892857143 + x = -1.229422463 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.892857143' to each side of the equation. -0.892857143 + 0.892857143 + x = -1.229422463 + 0.892857143 Combine like terms: -0.892857143 + 0.892857143 = 0.000000000 0.000000000 + x = -1.229422463 + 0.892857143 x = -1.229422463 + 0.892857143 Combine like terms: -1.229422463 + 0.892857143 = -0.33656532 x = -0.33656532 Simplifying x = -0.33656532Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.122279606, -0.33656532}
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