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Simplifying 2x2 + 5x + 3 = 18 Reorder the terms: 3 + 5x + 2x2 = 18 Solving 3 + 5x + 2x2 = 18 Solving for variable 'x'. Reorder the terms: 3 + -18 + 5x + 2x2 = 18 + -18 Combine like terms: 3 + -18 = -15 -15 + 5x + 2x2 = 18 + -18 Combine like terms: 18 + -18 = 0 -15 + 5x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -7.5 + 2.5x + x2 = 0 Move the constant term to the right: Add '7.5' to each side of the equation. -7.5 + 2.5x + 7.5 + x2 = 0 + 7.5 Reorder the terms: -7.5 + 7.5 + 2.5x + x2 = 0 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + 2.5x + x2 = 0 + 7.5 2.5x + x2 = 0 + 7.5 Combine like terms: 0 + 7.5 = 7.5 2.5x + x2 = 7.5 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 = 7.5 + 1.5625 Reorder the terms: 1.5625 + 2.5x + x2 = 7.5 + 1.5625 Combine like terms: 7.5 + 1.5625 = 9.0625 1.5625 + 2.5x + x2 = 9.0625 Factor a perfect square on the left side: (x + 1.25)(x + 1.25) = 9.0625 Calculate the square root of the right side: 3.010398645 Break this problem into two subproblems by setting (x + 1.25) equal to 3.010398645 and -3.010398645.Subproblem 1
x + 1.25 = 3.010398645 Simplifying x + 1.25 = 3.010398645 Reorder the terms: 1.25 + x = 3.010398645 Solving 1.25 + x = 3.010398645 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 = 3.010398645 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = 3.010398645 + -1.25 x = 3.010398645 + -1.25 Combine like terms: 3.010398645 + -1.25 = 1.760398645 x = 1.760398645 Simplifying x = 1.760398645Subproblem 2
x + 1.25 = -3.010398645 Simplifying x + 1.25 = -3.010398645 Reorder the terms: 1.25 + x = -3.010398645 Solving 1.25 + x = -3.010398645 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 = -3.010398645 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = -3.010398645 + -1.25 x = -3.010398645 + -1.25 Combine like terms: -3.010398645 + -1.25 = -4.260398645 x = -4.260398645 Simplifying x = -4.260398645Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.760398645, -4.260398645}
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