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Simplifying x2 + 3x + 2 = 130 Reorder the terms: 2 + 3x + x2 = 130 Solving 2 + 3x + x2 = 130 Solving for variable 'x'. Reorder the terms: 2 + -130 + 3x + x2 = 130 + -130 Combine like terms: 2 + -130 = -128 -128 + 3x + x2 = 130 + -130 Combine like terms: 130 + -130 = 0 -128 + 3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '128' to each side of the equation. -128 + 3x + 128 + x2 = 0 + 128 Reorder the terms: -128 + 128 + 3x + x2 = 0 + 128 Combine like terms: -128 + 128 = 0 0 + 3x + x2 = 0 + 128 3x + x2 = 0 + 128 Combine like terms: 0 + 128 = 128 3x + x2 = 128 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 = 128 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 128 + 2.25 Combine like terms: 128 + 2.25 = 130.25 2.25 + 3x + x2 = 130.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 130.25 Calculate the square root of the right side: 11.412712211 Break this problem into two subproblems by setting (x + 1.5) equal to 11.412712211 and -11.412712211.Subproblem 1
x + 1.5 = 11.412712211 Simplifying x + 1.5 = 11.412712211 Reorder the terms: 1.5 + x = 11.412712211 Solving 1.5 + x = 11.412712211 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 = 11.412712211 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 11.412712211 + -1.5 x = 11.412712211 + -1.5 Combine like terms: 11.412712211 + -1.5 = 9.912712211 x = 9.912712211 Simplifying x = 9.912712211Subproblem 2
x + 1.5 = -11.412712211 Simplifying x + 1.5 = -11.412712211 Reorder the terms: 1.5 + x = -11.412712211 Solving 1.5 + x = -11.412712211 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 = -11.412712211 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -11.412712211 + -1.5 x = -11.412712211 + -1.5 Combine like terms: -11.412712211 + -1.5 = -12.912712211 x = -12.912712211 Simplifying x = -12.912712211Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.912712211, -12.912712211}
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