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Simplifying 3x + -2 = 16x2 + -9 Reorder the terms: -2 + 3x = 16x2 + -9 Reorder the terms: -2 + 3x = -9 + 16x2 Solving -2 + 3x = -9 + 16x2 Solving for variable 'x'. Reorder the terms: -2 + 9 + 3x + -16x2 = -9 + 16x2 + 9 + -16x2 Combine like terms: -2 + 9 = 7 7 + 3x + -16x2 = -9 + 16x2 + 9 + -16x2 Reorder the terms: 7 + 3x + -16x2 = -9 + 9 + 16x2 + -16x2 Combine like terms: -9 + 9 = 0 7 + 3x + -16x2 = 0 + 16x2 + -16x2 7 + 3x + -16x2 = 16x2 + -16x2 Combine like terms: 16x2 + -16x2 = 0 7 + 3x + -16x2 = 0 Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. -0.4375 + -0.1875x + x2 = 0 Move the constant term to the right: Add '0.4375' to each side of the equation. -0.4375 + -0.1875x + 0.4375 + x2 = 0 + 0.4375 Reorder the terms: -0.4375 + 0.4375 + -0.1875x + x2 = 0 + 0.4375 Combine like terms: -0.4375 + 0.4375 = 0.0000 0.0000 + -0.1875x + x2 = 0 + 0.4375 -0.1875x + x2 = 0 + 0.4375 Combine like terms: 0 + 0.4375 = 0.4375 -0.1875x + x2 = 0.4375 The x term is -0.1875x. Take half its coefficient (-0.09375). Square it (0.0087890625) and add it to both sides. Add '0.0087890625' to each side of the equation. -0.1875x + 0.0087890625 + x2 = 0.4375 + 0.0087890625 Reorder the terms: 0.0087890625 + -0.1875x + x2 = 0.4375 + 0.0087890625 Combine like terms: 0.4375 + 0.0087890625 = 0.4462890625 0.0087890625 + -0.1875x + x2 = 0.4462890625 Factor a perfect square on the left side: (x + -0.09375)(x + -0.09375) = 0.4462890625 Calculate the square root of the right side: 0.668048698 Break this problem into two subproblems by setting (x + -0.09375) equal to 0.668048698 and -0.668048698.Subproblem 1
x + -0.09375 = 0.668048698 Simplifying x + -0.09375 = 0.668048698 Reorder the terms: -0.09375 + x = 0.668048698 Solving -0.09375 + x = 0.668048698 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.09375' to each side of the equation. -0.09375 + 0.09375 + x = 0.668048698 + 0.09375 Combine like terms: -0.09375 + 0.09375 = 0.00000 0.00000 + x = 0.668048698 + 0.09375 x = 0.668048698 + 0.09375 Combine like terms: 0.668048698 + 0.09375 = 0.761798698 x = 0.761798698 Simplifying x = 0.761798698Subproblem 2
x + -0.09375 = -0.668048698 Simplifying x + -0.09375 = -0.668048698 Reorder the terms: -0.09375 + x = -0.668048698 Solving -0.09375 + x = -0.668048698 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.09375' to each side of the equation. -0.09375 + 0.09375 + x = -0.668048698 + 0.09375 Combine like terms: -0.09375 + 0.09375 = 0.00000 0.00000 + x = -0.668048698 + 0.09375 x = -0.668048698 + 0.09375 Combine like terms: -0.668048698 + 0.09375 = -0.574298698 x = -0.574298698 Simplifying x = -0.574298698Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.761798698, -0.574298698}
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