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Simplifying 8x2 + 12x = 9 Reorder the terms: 12x + 8x2 = 9 Solving 12x + 8x2 = 9 Solving for variable 'x'. Reorder the terms: -9 + 12x + 8x2 = 9 + -9 Combine like terms: 9 + -9 = 0 -9 + 12x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -1.125 + 1.5x + x2 = 0 Move the constant term to the right: Add '1.125' to each side of the equation. -1.125 + 1.5x + 1.125 + x2 = 0 + 1.125 Reorder the terms: -1.125 + 1.125 + 1.5x + x2 = 0 + 1.125 Combine like terms: -1.125 + 1.125 = 0.000 0.000 + 1.5x + x2 = 0 + 1.125 1.5x + x2 = 0 + 1.125 Combine like terms: 0 + 1.125 = 1.125 1.5x + x2 = 1.125 The x term is 1.5x. Take half its coefficient (0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. 1.5x + 0.5625 + x2 = 1.125 + 0.5625 Reorder the terms: 0.5625 + 1.5x + x2 = 1.125 + 0.5625 Combine like terms: 1.125 + 0.5625 = 1.6875 0.5625 + 1.5x + x2 = 1.6875 Factor a perfect square on the left side: (x + 0.75)(x + 0.75) = 1.6875 Calculate the square root of the right side: 1.299038106 Break this problem into two subproblems by setting (x + 0.75) equal to 1.299038106 and -1.299038106.Subproblem 1
x + 0.75 = 1.299038106 Simplifying x + 0.75 = 1.299038106 Reorder the terms: 0.75 + x = 1.299038106 Solving 0.75 + x = 1.299038106 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = 1.299038106 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = 1.299038106 + -0.75 x = 1.299038106 + -0.75 Combine like terms: 1.299038106 + -0.75 = 0.549038106 x = 0.549038106 Simplifying x = 0.549038106Subproblem 2
x + 0.75 = -1.299038106 Simplifying x + 0.75 = -1.299038106 Reorder the terms: 0.75 + x = -1.299038106 Solving 0.75 + x = -1.299038106 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = -1.299038106 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = -1.299038106 + -0.75 x = -1.299038106 + -0.75 Combine like terms: -1.299038106 + -0.75 = -2.049038106 x = -2.049038106 Simplifying x = -2.049038106Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.549038106, -2.049038106}
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