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Simplifying 2x2 + 3x = 1120 Reorder the terms: 3x + 2x2 = 1120 Solving 3x + 2x2 = 1120 Solving for variable 'x'. Reorder the terms: -1120 + 3x + 2x2 = 1120 + -1120 Combine like terms: 1120 + -1120 = 0 -1120 + 3x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -560 + 1.5x + x2 = 0 Move the constant term to the right: Add '560' to each side of the equation. -560 + 1.5x + 560 + x2 = 0 + 560 Reorder the terms: -560 + 560 + 1.5x + x2 = 0 + 560 Combine like terms: -560 + 560 = 0 0 + 1.5x + x2 = 0 + 560 1.5x + x2 = 0 + 560 Combine like terms: 0 + 560 = 560 1.5x + x2 = 560 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 = 560 + 0.5625 Reorder the terms: 0.5625 + 1.5x + x2 = 560 + 0.5625 Combine like terms: 560 + 0.5625 = 560.5625 0.5625 + 1.5x + x2 = 560.5625 Factor a perfect square on the left side: (x + 0.75)(x + 0.75) = 560.5625 Calculate the square root of the right side: 23.676201131 Break this problem into two subproblems by setting (x + 0.75) equal to 23.676201131 and -23.676201131.Subproblem 1
x + 0.75 = 23.676201131 Simplifying x + 0.75 = 23.676201131 Reorder the terms: 0.75 + x = 23.676201131 Solving 0.75 + x = 23.676201131 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 = 23.676201131 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = 23.676201131 + -0.75 x = 23.676201131 + -0.75 Combine like terms: 23.676201131 + -0.75 = 22.926201131 x = 22.926201131 Simplifying x = 22.926201131Subproblem 2
x + 0.75 = -23.676201131 Simplifying x + 0.75 = -23.676201131 Reorder the terms: 0.75 + x = -23.676201131 Solving 0.75 + x = -23.676201131 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 = -23.676201131 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = -23.676201131 + -0.75 x = -23.676201131 + -0.75 Combine like terms: -23.676201131 + -0.75 = -24.426201131 x = -24.426201131 Simplifying x = -24.426201131Solution
The solution to the problem is based on the solutions from the subproblems. x = {22.926201131, -24.426201131}
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