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Simplifying 2x2 + 3x = 1225 Reorder the terms: 3x + 2x2 = 1225 Solving 3x + 2x2 = 1225 Solving for variable 'x'. Reorder the terms: -1225 + 3x + 2x2 = 1225 + -1225 Combine like terms: 1225 + -1225 = 0 -1225 + 3x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -612.5 + 1.5x + x2 = 0 Move the constant term to the right: Add '612.5' to each side of the equation. -612.5 + 1.5x + 612.5 + x2 = 0 + 612.5 Reorder the terms: -612.5 + 612.5 + 1.5x + x2 = 0 + 612.5 Combine like terms: -612.5 + 612.5 = 0.0 0.0 + 1.5x + x2 = 0 + 612.5 1.5x + x2 = 0 + 612.5 Combine like terms: 0 + 612.5 = 612.5 1.5x + x2 = 612.5 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 = 612.5 + 0.5625 Reorder the terms: 0.5625 + 1.5x + x2 = 612.5 + 0.5625 Combine like terms: 612.5 + 0.5625 = 613.0625 0.5625 + 1.5x + x2 = 613.0625 Factor a perfect square on the left side: (x + 0.75)(x + 0.75) = 613.0625 Calculate the square root of the right side: 24.76009895 Break this problem into two subproblems by setting (x + 0.75) equal to 24.76009895 and -24.76009895.Subproblem 1
x + 0.75 = 24.76009895 Simplifying x + 0.75 = 24.76009895 Reorder the terms: 0.75 + x = 24.76009895 Solving 0.75 + x = 24.76009895 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 = 24.76009895 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = 24.76009895 + -0.75 x = 24.76009895 + -0.75 Combine like terms: 24.76009895 + -0.75 = 24.01009895 x = 24.01009895 Simplifying x = 24.01009895Subproblem 2
x + 0.75 = -24.76009895 Simplifying x + 0.75 = -24.76009895 Reorder the terms: 0.75 + x = -24.76009895 Solving 0.75 + x = -24.76009895 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 = -24.76009895 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = -24.76009895 + -0.75 x = -24.76009895 + -0.75 Combine like terms: -24.76009895 + -0.75 = -25.51009895 x = -25.51009895 Simplifying x = -25.51009895Solution
The solution to the problem is based on the solutions from the subproblems. x = {24.01009895, -25.51009895}
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