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Simplifying 2x2 + 5x + -18 = 3 Reorder the terms: -18 + 5x + 2x2 = 3 Solving -18 + 5x + 2x2 = 3 Solving for variable 'x'. Reorder the terms: -18 + -3 + 5x + 2x2 = 3 + -3 Combine like terms: -18 + -3 = -21 -21 + 5x + 2x2 = 3 + -3 Combine like terms: 3 + -3 = 0 -21 + 5x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -10.5 + 2.5x + x2 = 0 Move the constant term to the right: Add '10.5' to each side of the equation. -10.5 + 2.5x + 10.5 + x2 = 0 + 10.5 Reorder the terms: -10.5 + 10.5 + 2.5x + x2 = 0 + 10.5 Combine like terms: -10.5 + 10.5 = 0.0 0.0 + 2.5x + x2 = 0 + 10.5 2.5x + x2 = 0 + 10.5 Combine like terms: 0 + 10.5 = 10.5 2.5x + x2 = 10.5 The x term is 2.5x. Take half its coefficient (1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. 2.5x + 1.5625 + x2 = 10.5 + 1.5625 Reorder the terms: 1.5625 + 2.5x + x2 = 10.5 + 1.5625 Combine like terms: 10.5 + 1.5625 = 12.0625 1.5625 + 2.5x + x2 = 12.0625 Factor a perfect square on the left side: (x + 1.25)(x + 1.25) = 12.0625 Calculate the square root of the right side: 3.473110997 Break this problem into two subproblems by setting (x + 1.25) equal to 3.473110997 and -3.473110997.Subproblem 1
x + 1.25 = 3.473110997 Simplifying x + 1.25 = 3.473110997 Reorder the terms: 1.25 + x = 3.473110997 Solving 1.25 + x = 3.473110997 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = 3.473110997 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = 3.473110997 + -1.25 x = 3.473110997 + -1.25 Combine like terms: 3.473110997 + -1.25 = 2.223110997 x = 2.223110997 Simplifying x = 2.223110997Subproblem 2
x + 1.25 = -3.473110997 Simplifying x + 1.25 = -3.473110997 Reorder the terms: 1.25 + x = -3.473110997 Solving 1.25 + x = -3.473110997 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = -3.473110997 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = -3.473110997 + -1.25 x = -3.473110997 + -1.25 Combine like terms: -3.473110997 + -1.25 = -4.723110997 x = -4.723110997 Simplifying x = -4.723110997Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.223110997, -4.723110997}
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