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Simplifying 7 + 10x + -9x2 = 0 Solving 7 + 10x + -9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -9 the coefficient of the squared term: Divide each side by '-9'. -0.7777777778 + -1.111111111x + x2 = 0 Move the constant term to the right: Add '0.7777777778' to each side of the equation. -0.7777777778 + -1.111111111x + 0.7777777778 + x2 = 0 + 0.7777777778 Reorder the terms: -0.7777777778 + 0.7777777778 + -1.111111111x + x2 = 0 + 0.7777777778 Combine like terms: -0.7777777778 + 0.7777777778 = 0.0000000000 0.0000000000 + -1.111111111x + x2 = 0 + 0.7777777778 -1.111111111x + x2 = 0 + 0.7777777778 Combine like terms: 0 + 0.7777777778 = 0.7777777778 -1.111111111x + x2 = 0.7777777778 The x term is -1.111111111x. Take half its coefficient (-0.5555555555). Square it (0.3086419752) and add it to both sides. Add '0.3086419752' to each side of the equation. -1.111111111x + 0.3086419752 + x2 = 0.7777777778 + 0.3086419752 Reorder the terms: 0.3086419752 + -1.111111111x + x2 = 0.7777777778 + 0.3086419752 Combine like terms: 0.7777777778 + 0.3086419752 = 1.086419753 0.3086419752 + -1.111111111x + x2 = 1.086419753 Factor a perfect square on the left side: (x + -0.5555555555)(x + -0.5555555555) = 1.086419753 Calculate the square root of the right side: 1.042314613 Break this problem into two subproblems by setting (x + -0.5555555555) equal to 1.042314613 and -1.042314613.Subproblem 1
x + -0.5555555555 = 1.042314613 Simplifying x + -0.5555555555 = 1.042314613 Reorder the terms: -0.5555555555 + x = 1.042314613 Solving -0.5555555555 + x = 1.042314613 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5555555555' to each side of the equation. -0.5555555555 + 0.5555555555 + x = 1.042314613 + 0.5555555555 Combine like terms: -0.5555555555 + 0.5555555555 = 0.0000000000 0.0000000000 + x = 1.042314613 + 0.5555555555 x = 1.042314613 + 0.5555555555 Combine like terms: 1.042314613 + 0.5555555555 = 1.5978701685 x = 1.5978701685 Simplifying x = 1.5978701685Subproblem 2
x + -0.5555555555 = -1.042314613 Simplifying x + -0.5555555555 = -1.042314613 Reorder the terms: -0.5555555555 + x = -1.042314613 Solving -0.5555555555 + x = -1.042314613 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5555555555' to each side of the equation. -0.5555555555 + 0.5555555555 + x = -1.042314613 + 0.5555555555 Combine like terms: -0.5555555555 + 0.5555555555 = 0.0000000000 0.0000000000 + x = -1.042314613 + 0.5555555555 x = -1.042314613 + 0.5555555555 Combine like terms: -1.042314613 + 0.5555555555 = -0.4867590575 x = -0.4867590575 Simplifying x = -0.4867590575Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.5978701685, -0.4867590575}
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