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Simplifying 2x2 + 3x + -37 = 9 Reorder the terms: -37 + 3x + 2x2 = 9 Solving -37 + 3x + 2x2 = 9 Solving for variable 'x'. Reorder the terms: -37 + -9 + 3x + 2x2 = 9 + -9 Combine like terms: -37 + -9 = -46 -46 + 3x + 2x2 = 9 + -9 Combine like terms: 9 + -9 = 0 -46 + 3x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -23 + 1.5x + x2 = 0 Move the constant term to the right: Add '23' to each side of the equation. -23 + 1.5x + 23 + x2 = 0 + 23 Reorder the terms: -23 + 23 + 1.5x + x2 = 0 + 23 Combine like terms: -23 + 23 = 0 0 + 1.5x + x2 = 0 + 23 1.5x + x2 = 0 + 23 Combine like terms: 0 + 23 = 23 1.5x + x2 = 23 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 = 23 + 0.5625 Reorder the terms: 0.5625 + 1.5x + x2 = 23 + 0.5625 Combine like terms: 23 + 0.5625 = 23.5625 0.5625 + 1.5x + x2 = 23.5625 Factor a perfect square on the left side: (x + 0.75)(x + 0.75) = 23.5625 Calculate the square root of the right side: 4.85412196 Break this problem into two subproblems by setting (x + 0.75) equal to 4.85412196 and -4.85412196.Subproblem 1
x + 0.75 = 4.85412196 Simplifying x + 0.75 = 4.85412196 Reorder the terms: 0.75 + x = 4.85412196 Solving 0.75 + x = 4.85412196 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 = 4.85412196 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = 4.85412196 + -0.75 x = 4.85412196 + -0.75 Combine like terms: 4.85412196 + -0.75 = 4.10412196 x = 4.10412196 Simplifying x = 4.10412196Subproblem 2
x + 0.75 = -4.85412196 Simplifying x + 0.75 = -4.85412196 Reorder the terms: 0.75 + x = -4.85412196 Solving 0.75 + x = -4.85412196 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 = -4.85412196 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = -4.85412196 + -0.75 x = -4.85412196 + -0.75 Combine like terms: -4.85412196 + -0.75 = -5.60412196 x = -5.60412196 Simplifying x = -5.60412196Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.10412196, -5.60412196}
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