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Simplifying 0.9x + -0.07x2 = -1 Solving 0.9x + -0.07x2 = -1 Solving for variable 'x'. Reorder the terms: 1 + 0.9x + -0.07x2 = -1 + 1 Combine like terms: -1 + 1 = 0 1 + 0.9x + -0.07x2 = 0 Begin completing the square. Divide all terms by -0.07 the coefficient of the squared term: Divide each side by '-0.07'. -14.28571429 + -12.85714286x + x2 = 0 Move the constant term to the right: Add '14.28571429' to each side of the equation. -14.28571429 + -12.85714286x + 14.28571429 + x2 = 0 + 14.28571429 Reorder the terms: -14.28571429 + 14.28571429 + -12.85714286x + x2 = 0 + 14.28571429 Combine like terms: -14.28571429 + 14.28571429 = 0.00000000 0.00000000 + -12.85714286x + x2 = 0 + 14.28571429 -12.85714286x + x2 = 0 + 14.28571429 Combine like terms: 0 + 14.28571429 = 14.28571429 -12.85714286x + x2 = 14.28571429 The x term is -12.85714286x. Take half its coefficient (-6.42857143). Square it (41.32653063) and add it to both sides. Add '41.32653063' to each side of the equation. -12.85714286x + 41.32653063 + x2 = 14.28571429 + 41.32653063 Reorder the terms: 41.32653063 + -12.85714286x + x2 = 14.28571429 + 41.32653063 Combine like terms: 14.28571429 + 41.32653063 = 55.61224492 41.32653063 + -12.85714286x + x2 = 55.61224492 Factor a perfect square on the left side: (x + -6.42857143)(x + -6.42857143) = 55.61224492 Calculate the square root of the right side: 7.457361794 Break this problem into two subproblems by setting (x + -6.42857143) equal to 7.457361794 and -7.457361794.Subproblem 1
x + -6.42857143 = 7.457361794 Simplifying x + -6.42857143 = 7.457361794 Reorder the terms: -6.42857143 + x = 7.457361794 Solving -6.42857143 + x = 7.457361794 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.42857143' to each side of the equation. -6.42857143 + 6.42857143 + x = 7.457361794 + 6.42857143 Combine like terms: -6.42857143 + 6.42857143 = 0.00000000 0.00000000 + x = 7.457361794 + 6.42857143 x = 7.457361794 + 6.42857143 Combine like terms: 7.457361794 + 6.42857143 = 13.885933224 x = 13.885933224 Simplifying x = 13.885933224Subproblem 2
x + -6.42857143 = -7.457361794 Simplifying x + -6.42857143 = -7.457361794 Reorder the terms: -6.42857143 + x = -7.457361794 Solving -6.42857143 + x = -7.457361794 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.42857143' to each side of the equation. -6.42857143 + 6.42857143 + x = -7.457361794 + 6.42857143 Combine like terms: -6.42857143 + 6.42857143 = 0.00000000 0.00000000 + x = -7.457361794 + 6.42857143 x = -7.457361794 + 6.42857143 Combine like terms: -7.457361794 + 6.42857143 = -1.028790364 x = -1.028790364 Simplifying x = -1.028790364Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.885933224, -1.028790364}
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