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Simplifying x2 + 3x + 12 = 90 Reorder the terms: 12 + 3x + x2 = 90 Solving 12 + 3x + x2 = 90 Solving for variable 'x'. Reorder the terms: 12 + -90 + 3x + x2 = 90 + -90 Combine like terms: 12 + -90 = -78 -78 + 3x + x2 = 90 + -90 Combine like terms: 90 + -90 = 0 -78 + 3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '78' to each side of the equation. -78 + 3x + 78 + x2 = 0 + 78 Reorder the terms: -78 + 78 + 3x + x2 = 0 + 78 Combine like terms: -78 + 78 = 0 0 + 3x + x2 = 0 + 78 3x + x2 = 0 + 78 Combine like terms: 0 + 78 = 78 3x + x2 = 78 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 = 78 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 78 + 2.25 Combine like terms: 78 + 2.25 = 80.25 2.25 + 3x + x2 = 80.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 80.25 Calculate the square root of the right side: 8.958236434 Break this problem into two subproblems by setting (x + 1.5) equal to 8.958236434 and -8.958236434.Subproblem 1
x + 1.5 = 8.958236434 Simplifying x + 1.5 = 8.958236434 Reorder the terms: 1.5 + x = 8.958236434 Solving 1.5 + x = 8.958236434 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 = 8.958236434 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 8.958236434 + -1.5 x = 8.958236434 + -1.5 Combine like terms: 8.958236434 + -1.5 = 7.458236434 x = 7.458236434 Simplifying x = 7.458236434Subproblem 2
x + 1.5 = -8.958236434 Simplifying x + 1.5 = -8.958236434 Reorder the terms: 1.5 + x = -8.958236434 Solving 1.5 + x = -8.958236434 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 = -8.958236434 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -8.958236434 + -1.5 x = -8.958236434 + -1.5 Combine like terms: -8.958236434 + -1.5 = -10.458236434 x = -10.458236434 Simplifying x = -10.458236434Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.458236434, -10.458236434}
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