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Simplifying 2x2 + 3x = 624 Reorder the terms: 3x + 2x2 = 624 Solving 3x + 2x2 = 624 Solving for variable 'x'. Reorder the terms: -624 + 3x + 2x2 = 624 + -624 Combine like terms: 624 + -624 = 0 -624 + 3x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -312 + 1.5x + x2 = 0 Move the constant term to the right: Add '312' to each side of the equation. -312 + 1.5x + 312 + x2 = 0 + 312 Reorder the terms: -312 + 312 + 1.5x + x2 = 0 + 312 Combine like terms: -312 + 312 = 0 0 + 1.5x + x2 = 0 + 312 1.5x + x2 = 0 + 312 Combine like terms: 0 + 312 = 312 1.5x + x2 = 312 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 = 312 + 0.5625 Reorder the terms: 0.5625 + 1.5x + x2 = 312 + 0.5625 Combine like terms: 312 + 0.5625 = 312.5625 0.5625 + 1.5x + x2 = 312.5625 Factor a perfect square on the left side: (x + 0.75)(x + 0.75) = 312.5625 Calculate the square root of the right side: 17.679437208 Break this problem into two subproblems by setting (x + 0.75) equal to 17.679437208 and -17.679437208.Subproblem 1
x + 0.75 = 17.679437208 Simplifying x + 0.75 = 17.679437208 Reorder the terms: 0.75 + x = 17.679437208 Solving 0.75 + x = 17.679437208 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 = 17.679437208 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = 17.679437208 + -0.75 x = 17.679437208 + -0.75 Combine like terms: 17.679437208 + -0.75 = 16.929437208 x = 16.929437208 Simplifying x = 16.929437208Subproblem 2
x + 0.75 = -17.679437208 Simplifying x + 0.75 = -17.679437208 Reorder the terms: 0.75 + x = -17.679437208 Solving 0.75 + x = -17.679437208 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 = -17.679437208 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = -17.679437208 + -0.75 x = -17.679437208 + -0.75 Combine like terms: -17.679437208 + -0.75 = -18.429437208 x = -18.429437208 Simplifying x = -18.429437208Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.929437208, -18.429437208}
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