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Simplifying (8x2 + -7x + 13) + (9x2 + 9x + -81) = 0 Reorder the terms: (13 + -7x + 8x2) + (9x2 + 9x + -81) = 0 Remove parenthesis around (13 + -7x + 8x2) 13 + -7x + 8x2 + (9x2 + 9x + -81) = 0 Reorder the terms: 13 + -7x + 8x2 + (-81 + 9x + 9x2) = 0 Remove parenthesis around (-81 + 9x + 9x2) 13 + -7x + 8x2 + -81 + 9x + 9x2 = 0 Reorder the terms: 13 + -81 + -7x + 9x + 8x2 + 9x2 = 0 Combine like terms: 13 + -81 = -68 -68 + -7x + 9x + 8x2 + 9x2 = 0 Combine like terms: -7x + 9x = 2x -68 + 2x + 8x2 + 9x2 = 0 Combine like terms: 8x2 + 9x2 = 17x2 -68 + 2x + 17x2 = 0 Solving -68 + 2x + 17x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 17 the coefficient of the squared term: Divide each side by '17'. -4 + 0.1176470588x + x2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + 0.1176470588x + 4 + x2 = 0 + 4 Reorder the terms: -4 + 4 + 0.1176470588x + x2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 0.1176470588x + x2 = 0 + 4 0.1176470588x + x2 = 0 + 4 Combine like terms: 0 + 4 = 4 0.1176470588x + x2 = 4 The x term is 0.1176470588x. Take half its coefficient (0.0588235294). Square it (0.003460207611) and add it to both sides. Add '0.003460207611' to each side of the equation. 0.1176470588x + 0.003460207611 + x2 = 4 + 0.003460207611 Reorder the terms: 0.003460207611 + 0.1176470588x + x2 = 4 + 0.003460207611 Combine like terms: 4 + 0.003460207611 = 4.003460207611 0.003460207611 + 0.1176470588x + x2 = 4.003460207611 Factor a perfect square on the left side: (x + 0.0588235294)(x + 0.0588235294) = 4.003460207611 Calculate the square root of the right side: 2.000864865 Break this problem into two subproblems by setting (x + 0.0588235294) equal to 2.000864865 and -2.000864865.Subproblem 1
x + 0.0588235294 = 2.000864865 Simplifying x + 0.0588235294 = 2.000864865 Reorder the terms: 0.0588235294 + x = 2.000864865 Solving 0.0588235294 + x = 2.000864865 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.0588235294' to each side of the equation. 0.0588235294 + -0.0588235294 + x = 2.000864865 + -0.0588235294 Combine like terms: 0.0588235294 + -0.0588235294 = 0.0000000000 0.0000000000 + x = 2.000864865 + -0.0588235294 x = 2.000864865 + -0.0588235294 Combine like terms: 2.000864865 + -0.0588235294 = 1.9420413356 x = 1.9420413356 Simplifying x = 1.9420413356Subproblem 2
x + 0.0588235294 = -2.000864865 Simplifying x + 0.0588235294 = -2.000864865 Reorder the terms: 0.0588235294 + x = -2.000864865 Solving 0.0588235294 + x = -2.000864865 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.0588235294' to each side of the equation. 0.0588235294 + -0.0588235294 + x = -2.000864865 + -0.0588235294 Combine like terms: 0.0588235294 + -0.0588235294 = 0.0000000000 0.0000000000 + x = -2.000864865 + -0.0588235294 x = -2.000864865 + -0.0588235294 Combine like terms: -2.000864865 + -0.0588235294 = -2.0596883944 x = -2.0596883944 Simplifying x = -2.0596883944Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.9420413356, -2.0596883944}
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