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Simplifying 9x2 + 12x + -6 = x2 + -7 Reorder the terms: -6 + 12x + 9x2 = x2 + -7 Reorder the terms: -6 + 12x + 9x2 = -7 + x2 Solving -6 + 12x + 9x2 = -7 + x2 Solving for variable 'x'. Reorder the terms: -6 + 7 + 12x + 9x2 + -1x2 = -7 + x2 + 7 + -1x2 Combine like terms: -6 + 7 = 1 1 + 12x + 9x2 + -1x2 = -7 + x2 + 7 + -1x2 Combine like terms: 9x2 + -1x2 = 8x2 1 + 12x + 8x2 = -7 + x2 + 7 + -1x2 Reorder the terms: 1 + 12x + 8x2 = -7 + 7 + x2 + -1x2 Combine like terms: -7 + 7 = 0 1 + 12x + 8x2 = 0 + x2 + -1x2 1 + 12x + 8x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 1 + 12x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 0.125 + 1.5x + x2 = 0 Move the constant term to the right: Add '-0.125' to each side of the equation. 0.125 + 1.5x + -0.125 + x2 = 0 + -0.125 Reorder the terms: 0.125 + -0.125 + 1.5x + x2 = 0 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + 1.5x + x2 = 0 + -0.125 1.5x + x2 = 0 + -0.125 Combine like terms: 0 + -0.125 = -0.125 1.5x + x2 = -0.125 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 = -0.125 + 0.5625 Reorder the terms: 0.5625 + 1.5x + x2 = -0.125 + 0.5625 Combine like terms: -0.125 + 0.5625 = 0.4375 0.5625 + 1.5x + x2 = 0.4375 Factor a perfect square on the left side: (x + 0.75)(x + 0.75) = 0.4375 Calculate the square root of the right side: 0.661437828 Break this problem into two subproblems by setting (x + 0.75) equal to 0.661437828 and -0.661437828.Subproblem 1
x + 0.75 = 0.661437828 Simplifying x + 0.75 = 0.661437828 Reorder the terms: 0.75 + x = 0.661437828 Solving 0.75 + x = 0.661437828 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 = 0.661437828 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = 0.661437828 + -0.75 x = 0.661437828 + -0.75 Combine like terms: 0.661437828 + -0.75 = -0.088562172 x = -0.088562172 Simplifying x = -0.088562172Subproblem 2
x + 0.75 = -0.661437828 Simplifying x + 0.75 = -0.661437828 Reorder the terms: 0.75 + x = -0.661437828 Solving 0.75 + x = -0.661437828 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 = -0.661437828 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = -0.661437828 + -0.75 x = -0.661437828 + -0.75 Combine like terms: -0.661437828 + -0.75 = -1.411437828 x = -1.411437828 Simplifying x = -1.411437828Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.088562172, -1.411437828}
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