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Simplifying 2x2 + 6x + 9 = 42 Reorder the terms: 9 + 6x + 2x2 = 42 Solving 9 + 6x + 2x2 = 42 Solving for variable 'x'. Reorder the terms: 9 + -42 + 6x + 2x2 = 42 + -42 Combine like terms: 9 + -42 = -33 -33 + 6x + 2x2 = 42 + -42 Combine like terms: 42 + -42 = 0 -33 + 6x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -16.5 + 3x + x2 = 0 Move the constant term to the right: Add '16.5' to each side of the equation. -16.5 + 3x + 16.5 + x2 = 0 + 16.5 Reorder the terms: -16.5 + 16.5 + 3x + x2 = 0 + 16.5 Combine like terms: -16.5 + 16.5 = 0.0 0.0 + 3x + x2 = 0 + 16.5 3x + x2 = 0 + 16.5 Combine like terms: 0 + 16.5 = 16.5 3x + x2 = 16.5 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = 16.5 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 16.5 + 2.25 Combine like terms: 16.5 + 2.25 = 18.75 2.25 + 3x + x2 = 18.75 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 18.75 Calculate the square root of the right side: 4.330127019 Break this problem into two subproblems by setting (x + 1.5) equal to 4.330127019 and -4.330127019.Subproblem 1
x + 1.5 = 4.330127019 Simplifying x + 1.5 = 4.330127019 Reorder the terms: 1.5 + x = 4.330127019 Solving 1.5 + x = 4.330127019 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 4.330127019 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 4.330127019 + -1.5 x = 4.330127019 + -1.5 Combine like terms: 4.330127019 + -1.5 = 2.830127019 x = 2.830127019 Simplifying x = 2.830127019Subproblem 2
x + 1.5 = -4.330127019 Simplifying x + 1.5 = -4.330127019 Reorder the terms: 1.5 + x = -4.330127019 Solving 1.5 + x = -4.330127019 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -4.330127019 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -4.330127019 + -1.5 x = -4.330127019 + -1.5 Combine like terms: -4.330127019 + -1.5 = -5.830127019 x = -5.830127019 Simplifying x = -5.830127019Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.830127019, -5.830127019}
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