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Simplifying 25x2 + -30x + 9 = 27 Reorder the terms: 9 + -30x + 25x2 = 27 Solving 9 + -30x + 25x2 = 27 Solving for variable 'x'. Reorder the terms: 9 + -27 + -30x + 25x2 = 27 + -27 Combine like terms: 9 + -27 = -18 -18 + -30x + 25x2 = 27 + -27 Combine like terms: 27 + -27 = 0 -18 + -30x + 25x2 = 0 Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. -0.72 + -1.2x + x2 = 0 Move the constant term to the right: Add '0.72' to each side of the equation. -0.72 + -1.2x + 0.72 + x2 = 0 + 0.72 Reorder the terms: -0.72 + 0.72 + -1.2x + x2 = 0 + 0.72 Combine like terms: -0.72 + 0.72 = 0.00 0.00 + -1.2x + x2 = 0 + 0.72 -1.2x + x2 = 0 + 0.72 Combine like terms: 0 + 0.72 = 0.72 -1.2x + x2 = 0.72 The x term is -1.2x. Take half its coefficient (-0.6). Square it (0.36) and add it to both sides. Add '0.36' to each side of the equation. -1.2x + 0.36 + x2 = 0.72 + 0.36 Reorder the terms: 0.36 + -1.2x + x2 = 0.72 + 0.36 Combine like terms: 0.72 + 0.36 = 1.08 0.36 + -1.2x + x2 = 1.08 Factor a perfect square on the left side: (x + -0.6)(x + -0.6) = 1.08 Calculate the square root of the right side: 1.039230485 Break this problem into two subproblems by setting (x + -0.6) equal to 1.039230485 and -1.039230485.Subproblem 1
x + -0.6 = 1.039230485 Simplifying x + -0.6 = 1.039230485 Reorder the terms: -0.6 + x = 1.039230485 Solving -0.6 + x = 1.039230485 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6' to each side of the equation. -0.6 + 0.6 + x = 1.039230485 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + x = 1.039230485 + 0.6 x = 1.039230485 + 0.6 Combine like terms: 1.039230485 + 0.6 = 1.639230485 x = 1.639230485 Simplifying x = 1.639230485Subproblem 2
x + -0.6 = -1.039230485 Simplifying x + -0.6 = -1.039230485 Reorder the terms: -0.6 + x = -1.039230485 Solving -0.6 + x = -1.039230485 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6' to each side of the equation. -0.6 + 0.6 + x = -1.039230485 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + x = -1.039230485 + 0.6 x = -1.039230485 + 0.6 Combine like terms: -1.039230485 + 0.6 = -0.439230485 x = -0.439230485 Simplifying x = -0.439230485Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.639230485, -0.439230485}
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