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Simplifying 8x2 + -7x + -9 = 0 Reorder the terms: -9 + -7x + 8x2 = 0 Solving -9 + -7x + 8x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -1.125 + -0.875x + x2 = 0 Move the constant term to the right: Add '1.125' to each side of the equation. -1.125 + -0.875x + 1.125 + x2 = 0 + 1.125 Reorder the terms: -1.125 + 1.125 + -0.875x + x2 = 0 + 1.125 Combine like terms: -1.125 + 1.125 = 0.000 0.000 + -0.875x + x2 = 0 + 1.125 -0.875x + x2 = 0 + 1.125 Combine like terms: 0 + 1.125 = 1.125 -0.875x + x2 = 1.125 The x term is -0.875x. Take half its coefficient (-0.4375). Square it (0.19140625) and add it to both sides. Add '0.19140625' to each side of the equation. -0.875x + 0.19140625 + x2 = 1.125 + 0.19140625 Reorder the terms: 0.19140625 + -0.875x + x2 = 1.125 + 0.19140625 Combine like terms: 1.125 + 0.19140625 = 1.31640625 0.19140625 + -0.875x + x2 = 1.31640625 Factor a perfect square on the left side: (x + -0.4375)(x + -0.4375) = 1.31640625 Calculate the square root of the right side: 1.147347484 Break this problem into two subproblems by setting (x + -0.4375) equal to 1.147347484 and -1.147347484.Subproblem 1
x + -0.4375 = 1.147347484 Simplifying x + -0.4375 = 1.147347484 Reorder the terms: -0.4375 + x = 1.147347484 Solving -0.4375 + x = 1.147347484 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4375' to each side of the equation. -0.4375 + 0.4375 + x = 1.147347484 + 0.4375 Combine like terms: -0.4375 + 0.4375 = 0.0000 0.0000 + x = 1.147347484 + 0.4375 x = 1.147347484 + 0.4375 Combine like terms: 1.147347484 + 0.4375 = 1.584847484 x = 1.584847484 Simplifying x = 1.584847484Subproblem 2
x + -0.4375 = -1.147347484 Simplifying x + -0.4375 = -1.147347484 Reorder the terms: -0.4375 + x = -1.147347484 Solving -0.4375 + x = -1.147347484 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4375' to each side of the equation. -0.4375 + 0.4375 + x = -1.147347484 + 0.4375 Combine like terms: -0.4375 + 0.4375 = 0.0000 0.0000 + x = -1.147347484 + 0.4375 x = -1.147347484 + 0.4375 Combine like terms: -1.147347484 + 0.4375 = -0.709847484 x = -0.709847484 Simplifying x = -0.709847484Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.584847484, -0.709847484}
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