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Simplifying 8x2 + 3x + -9 = 0 Reorder the terms: -9 + 3x + 8x2 = 0 Solving -9 + 3x + 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 + 0.375x + x2 = 0 Move the constant term to the right: Add '1.125' to each side of the equation. -1.125 + 0.375x + 1.125 + x2 = 0 + 1.125 Reorder the terms: -1.125 + 1.125 + 0.375x + x2 = 0 + 1.125 Combine like terms: -1.125 + 1.125 = 0.000 0.000 + 0.375x + x2 = 0 + 1.125 0.375x + x2 = 0 + 1.125 Combine like terms: 0 + 1.125 = 1.125 0.375x + x2 = 1.125 The x term is 0.375x. Take half its coefficient (0.1875). Square it (0.03515625) and add it to both sides. Add '0.03515625' to each side of the equation. 0.375x + 0.03515625 + x2 = 1.125 + 0.03515625 Reorder the terms: 0.03515625 + 0.375x + x2 = 1.125 + 0.03515625 Combine like terms: 1.125 + 0.03515625 = 1.16015625 0.03515625 + 0.375x + x2 = 1.16015625 Factor a perfect square on the left side: (x + 0.1875)(x + 0.1875) = 1.16015625 Calculate the square root of the right side: 1.077105496 Break this problem into two subproblems by setting (x + 0.1875) equal to 1.077105496 and -1.077105496.Subproblem 1
x + 0.1875 = 1.077105496 Simplifying x + 0.1875 = 1.077105496 Reorder the terms: 0.1875 + x = 1.077105496 Solving 0.1875 + x = 1.077105496 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1875' to each side of the equation. 0.1875 + -0.1875 + x = 1.077105496 + -0.1875 Combine like terms: 0.1875 + -0.1875 = 0.0000 0.0000 + x = 1.077105496 + -0.1875 x = 1.077105496 + -0.1875 Combine like terms: 1.077105496 + -0.1875 = 0.889605496 x = 0.889605496 Simplifying x = 0.889605496Subproblem 2
x + 0.1875 = -1.077105496 Simplifying x + 0.1875 = -1.077105496 Reorder the terms: 0.1875 + x = -1.077105496 Solving 0.1875 + x = -1.077105496 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1875' to each side of the equation. 0.1875 + -0.1875 + x = -1.077105496 + -0.1875 Combine like terms: 0.1875 + -0.1875 = 0.0000 0.0000 + x = -1.077105496 + -0.1875 x = -1.077105496 + -0.1875 Combine like terms: -1.077105496 + -0.1875 = -1.264605496 x = -1.264605496 Simplifying x = -1.264605496Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.889605496, -1.264605496}
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