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Simplifying (2x2 + -3x + -8) + -1(-7x2 + 7x + 7) = 0 Reorder the terms: (-8 + -3x + 2x2) + -1(-7x2 + 7x + 7) = 0 Remove parenthesis around (-8 + -3x + 2x2) -8 + -3x + 2x2 + -1(-7x2 + 7x + 7) = 0 Reorder the terms: -8 + -3x + 2x2 + -1(7 + 7x + -7x2) = 0 -8 + -3x + 2x2 + (7 * -1 + 7x * -1 + -7x2 * -1) = 0 -8 + -3x + 2x2 + (-7 + -7x + 7x2) = 0 Reorder the terms: -8 + -7 + -3x + -7x + 2x2 + 7x2 = 0 Combine like terms: -8 + -7 = -15 -15 + -3x + -7x + 2x2 + 7x2 = 0 Combine like terms: -3x + -7x = -10x -15 + -10x + 2x2 + 7x2 = 0 Combine like terms: 2x2 + 7x2 = 9x2 -15 + -10x + 9x2 = 0 Solving -15 + -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'. -1.666666667 + -1.111111111x + x2 = 0 Move the constant term to the right: Add '1.666666667' to each side of the equation. -1.666666667 + -1.111111111x + 1.666666667 + x2 = 0 + 1.666666667 Reorder the terms: -1.666666667 + 1.666666667 + -1.111111111x + x2 = 0 + 1.666666667 Combine like terms: -1.666666667 + 1.666666667 = 0.000000000 0.000000000 + -1.111111111x + x2 = 0 + 1.666666667 -1.111111111x + x2 = 0 + 1.666666667 Combine like terms: 0 + 1.666666667 = 1.666666667 -1.111111111x + x2 = 1.666666667 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 = 1.666666667 + 0.3086419752 Reorder the terms: 0.3086419752 + -1.111111111x + x2 = 1.666666667 + 0.3086419752 Combine like terms: 1.666666667 + 0.3086419752 = 1.9753086422 0.3086419752 + -1.111111111x + x2 = 1.9753086422 Factor a perfect square on the left side: (x + -0.5555555555)(x + -0.5555555555) = 1.9753086422 Calculate the square root of the right side: 1.405456738 Break this problem into two subproblems by setting (x + -0.5555555555) equal to 1.405456738 and -1.405456738.Subproblem 1
x + -0.5555555555 = 1.405456738 Simplifying x + -0.5555555555 = 1.405456738 Reorder the terms: -0.5555555555 + x = 1.405456738 Solving -0.5555555555 + x = 1.405456738 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 = 1.405456738 + 0.5555555555 Combine like terms: -0.5555555555 + 0.5555555555 = 0.0000000000 0.0000000000 + x = 1.405456738 + 0.5555555555 x = 1.405456738 + 0.5555555555 Combine like terms: 1.405456738 + 0.5555555555 = 1.9610122935 x = 1.9610122935 Simplifying x = 1.9610122935Subproblem 2
x + -0.5555555555 = -1.405456738 Simplifying x + -0.5555555555 = -1.405456738 Reorder the terms: -0.5555555555 + x = -1.405456738 Solving -0.5555555555 + x = -1.405456738 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 = -1.405456738 + 0.5555555555 Combine like terms: -0.5555555555 + 0.5555555555 = 0.0000000000 0.0000000000 + x = -1.405456738 + 0.5555555555 x = -1.405456738 + 0.5555555555 Combine like terms: -1.405456738 + 0.5555555555 = -0.8499011825 x = -0.8499011825 Simplifying x = -0.8499011825Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.9610122935, -0.8499011825}
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