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Simplifying x(2x + 3) = 160 Reorder the terms: x(3 + 2x) = 160 (3 * x + 2x * x) = 160 (3x + 2x2) = 160 Solving 3x + 2x2 = 160 Solving for variable 'x'. Reorder the terms: -160 + 3x + 2x2 = 160 + -160 Combine like terms: 160 + -160 = 0 -160 + 3x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -80 + 1.5x + x2 = 0 Move the constant term to the right: Add '80' to each side of the equation. -80 + 1.5x + 80 + x2 = 0 + 80 Reorder the terms: -80 + 80 + 1.5x + x2 = 0 + 80 Combine like terms: -80 + 80 = 0 0 + 1.5x + x2 = 0 + 80 1.5x + x2 = 0 + 80 Combine like terms: 0 + 80 = 80 1.5x + x2 = 80 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 = 80 + 0.5625 Reorder the terms: 0.5625 + 1.5x + x2 = 80 + 0.5625 Combine like terms: 80 + 0.5625 = 80.5625 0.5625 + 1.5x + x2 = 80.5625 Factor a perfect square on the left side: (x + 0.75)(x + 0.75) = 80.5625 Calculate the square root of the right side: 8.975661536 Break this problem into two subproblems by setting (x + 0.75) equal to 8.975661536 and -8.975661536.Subproblem 1
x + 0.75 = 8.975661536 Simplifying x + 0.75 = 8.975661536 Reorder the terms: 0.75 + x = 8.975661536 Solving 0.75 + x = 8.975661536 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 = 8.975661536 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = 8.975661536 + -0.75 x = 8.975661536 + -0.75 Combine like terms: 8.975661536 + -0.75 = 8.225661536 x = 8.225661536 Simplifying x = 8.225661536Subproblem 2
x + 0.75 = -8.975661536 Simplifying x + 0.75 = -8.975661536 Reorder the terms: 0.75 + x = -8.975661536 Solving 0.75 + x = -8.975661536 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 = -8.975661536 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = -8.975661536 + -0.75 x = -8.975661536 + -0.75 Combine like terms: -8.975661536 + -0.75 = -9.725661536 x = -9.725661536 Simplifying x = -9.725661536Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.225661536, -9.725661536}
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