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Simplifying (7x2 + 8x + -5) + (9x2 + -9x) = 0 Reorder the terms: (-5 + 8x + 7x2) + (9x2 + -9x) = 0 Remove parenthesis around (-5 + 8x + 7x2) -5 + 8x + 7x2 + (9x2 + -9x) = 0 Reorder the terms: -5 + 8x + 7x2 + (-9x + 9x2) = 0 Remove parenthesis around (-9x + 9x2) -5 + 8x + 7x2 + -9x + 9x2 = 0 Reorder the terms: -5 + 8x + -9x + 7x2 + 9x2 = 0 Combine like terms: 8x + -9x = -1x -5 + -1x + 7x2 + 9x2 = 0 Combine like terms: 7x2 + 9x2 = 16x2 -5 + -1x + 16x2 = 0 Solving -5 + -1x + 16x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -0.3125 + -0.0625x + x2 = 0 Move the constant term to the right: Add '0.3125' to each side of the equation. -0.3125 + -0.0625x + 0.3125 + x2 = 0 + 0.3125 Reorder the terms: -0.3125 + 0.3125 + -0.0625x + x2 = 0 + 0.3125 Combine like terms: -0.3125 + 0.3125 = 0.0000 0.0000 + -0.0625x + x2 = 0 + 0.3125 -0.0625x + x2 = 0 + 0.3125 Combine like terms: 0 + 0.3125 = 0.3125 -0.0625x + x2 = 0.3125 The x term is -0.0625x. Take half its coefficient (-0.03125). Square it (0.0009765625) and add it to both sides. Add '0.0009765625' to each side of the equation. -0.0625x + 0.0009765625 + x2 = 0.3125 + 0.0009765625 Reorder the terms: 0.0009765625 + -0.0625x + x2 = 0.3125 + 0.0009765625 Combine like terms: 0.3125 + 0.0009765625 = 0.3134765625 0.0009765625 + -0.0625x + x2 = 0.3134765625 Factor a perfect square on the left side: (x + -0.03125)(x + -0.03125) = 0.3134765625 Calculate the square root of the right side: 0.559889777 Break this problem into two subproblems by setting (x + -0.03125) equal to 0.559889777 and -0.559889777.Subproblem 1
x + -0.03125 = 0.559889777 Simplifying x + -0.03125 = 0.559889777 Reorder the terms: -0.03125 + x = 0.559889777 Solving -0.03125 + x = 0.559889777 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.03125' to each side of the equation. -0.03125 + 0.03125 + x = 0.559889777 + 0.03125 Combine like terms: -0.03125 + 0.03125 = 0.00000 0.00000 + x = 0.559889777 + 0.03125 x = 0.559889777 + 0.03125 Combine like terms: 0.559889777 + 0.03125 = 0.591139777 x = 0.591139777 Simplifying x = 0.591139777Subproblem 2
x + -0.03125 = -0.559889777 Simplifying x + -0.03125 = -0.559889777 Reorder the terms: -0.03125 + x = -0.559889777 Solving -0.03125 + x = -0.559889777 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.03125' to each side of the equation. -0.03125 + 0.03125 + x = -0.559889777 + 0.03125 Combine like terms: -0.03125 + 0.03125 = 0.00000 0.00000 + x = -0.559889777 + 0.03125 x = -0.559889777 + 0.03125 Combine like terms: -0.559889777 + 0.03125 = -0.528639777 x = -0.528639777 Simplifying x = -0.528639777Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.591139777, -0.528639777}
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