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Simplifying 0.9x + -0.9x2 = -1 Solving 0.9x + -0.9x2 = -1 Solving for variable 'x'. Reorder the terms: 1 + 0.9x + -0.9x2 = -1 + 1 Combine like terms: -1 + 1 = 0 1 + 0.9x + -0.9x2 = 0 Begin completing the square. Divide all terms by -0.9 the coefficient of the squared term: Divide each side by '-0.9'. -1.111111111 + -1x + x2 = 0 Move the constant term to the right: Add '1.111111111' to each side of the equation. -1.111111111 + -1x + 1.111111111 + x2 = 0 + 1.111111111 Reorder the terms: -1.111111111 + 1.111111111 + -1x + x2 = 0 + 1.111111111 Combine like terms: -1.111111111 + 1.111111111 = 0.000000000 0.000000000 + -1x + x2 = 0 + 1.111111111 -1x + x2 = 0 + 1.111111111 Combine like terms: 0 + 1.111111111 = 1.111111111 -1x + x2 = 1.111111111 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = 1.111111111 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 1.111111111 + 0.25 Combine like terms: 1.111111111 + 0.25 = 1.361111111 0.25 + -1x + x2 = 1.361111111 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 1.361111111 Calculate the square root of the right side: 1.166666667 Break this problem into two subproblems by setting (x + -0.5) equal to 1.166666667 and -1.166666667.Subproblem 1
x + -0.5 = 1.166666667 Simplifying x + -0.5 = 1.166666667 Reorder the terms: -0.5 + x = 1.166666667 Solving -0.5 + x = 1.166666667 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 1.166666667 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 1.166666667 + 0.5 x = 1.166666667 + 0.5 Combine like terms: 1.166666667 + 0.5 = 1.666666667 x = 1.666666667 Simplifying x = 1.666666667Subproblem 2
x + -0.5 = -1.166666667 Simplifying x + -0.5 = -1.166666667 Reorder the terms: -0.5 + x = -1.166666667 Solving -0.5 + x = -1.166666667 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -1.166666667 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -1.166666667 + 0.5 x = -1.166666667 + 0.5 Combine like terms: -1.166666667 + 0.5 = -0.666666667 x = -0.666666667 Simplifying x = -0.666666667Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.666666667, -0.666666667}
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