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Simplifying 0.9x + -0.7x2 = -1 Solving 0.9x + -0.7x2 = -1 Solving for variable 'x'. Reorder the terms: 1 + 0.9x + -0.7x2 = -1 + 1 Combine like terms: -1 + 1 = 0 1 + 0.9x + -0.7x2 = 0 Begin completing the square. Divide all terms by -0.7 the coefficient of the squared term: Divide each side by '-0.7'. -1.428571429 + -1.285714286x + x2 = 0 Move the constant term to the right: Add '1.428571429' to each side of the equation. -1.428571429 + -1.285714286x + 1.428571429 + x2 = 0 + 1.428571429 Reorder the terms: -1.428571429 + 1.428571429 + -1.285714286x + x2 = 0 + 1.428571429 Combine like terms: -1.428571429 + 1.428571429 = 0.000000000 0.000000000 + -1.285714286x + x2 = 0 + 1.428571429 -1.285714286x + x2 = 0 + 1.428571429 Combine like terms: 0 + 1.428571429 = 1.428571429 -1.285714286x + x2 = 1.428571429 The x term is -1.285714286x. Take half its coefficient (-0.642857143). Square it (0.4132653063) and add it to both sides. Add '0.4132653063' to each side of the equation. -1.285714286x + 0.4132653063 + x2 = 1.428571429 + 0.4132653063 Reorder the terms: 0.4132653063 + -1.285714286x + x2 = 1.428571429 + 0.4132653063 Combine like terms: 1.428571429 + 0.4132653063 = 1.8418367353 0.4132653063 + -1.285714286x + x2 = 1.8418367353 Factor a perfect square on the left side: (x + -0.642857143)(x + -0.642857143) = 1.8418367353 Calculate the square root of the right side: 1.357142857 Break this problem into two subproblems by setting (x + -0.642857143) equal to 1.357142857 and -1.357142857.Subproblem 1
x + -0.642857143 = 1.357142857 Simplifying x + -0.642857143 = 1.357142857 Reorder the terms: -0.642857143 + x = 1.357142857 Solving -0.642857143 + x = 1.357142857 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.642857143' to each side of the equation. -0.642857143 + 0.642857143 + x = 1.357142857 + 0.642857143 Combine like terms: -0.642857143 + 0.642857143 = 0.000000000 0.000000000 + x = 1.357142857 + 0.642857143 x = 1.357142857 + 0.642857143 Combine like terms: 1.357142857 + 0.642857143 = 2 x = 2 Simplifying x = 2Subproblem 2
x + -0.642857143 = -1.357142857 Simplifying x + -0.642857143 = -1.357142857 Reorder the terms: -0.642857143 + x = -1.357142857 Solving -0.642857143 + x = -1.357142857 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.642857143' to each side of the equation. -0.642857143 + 0.642857143 + x = -1.357142857 + 0.642857143 Combine like terms: -0.642857143 + 0.642857143 = 0.000000000 0.000000000 + x = -1.357142857 + 0.642857143 x = -1.357142857 + 0.642857143 Combine like terms: -1.357142857 + 0.642857143 = -0.714285714 x = -0.714285714 Simplifying x = -0.714285714Solution
The solution to the problem is based on the solutions from the subproblems. x = {2, -0.714285714}
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