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Simplifying x2 + 3x + 5 = 170 Reorder the terms: 5 + 3x + x2 = 170 Solving 5 + 3x + x2 = 170 Solving for variable 'x'. Reorder the terms: 5 + -170 + 3x + x2 = 170 + -170 Combine like terms: 5 + -170 = -165 -165 + 3x + x2 = 170 + -170 Combine like terms: 170 + -170 = 0 -165 + 3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '165' to each side of the equation. -165 + 3x + 165 + x2 = 0 + 165 Reorder the terms: -165 + 165 + 3x + x2 = 0 + 165 Combine like terms: -165 + 165 = 0 0 + 3x + x2 = 0 + 165 3x + x2 = 0 + 165 Combine like terms: 0 + 165 = 165 3x + x2 = 165 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 = 165 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 165 + 2.25 Combine like terms: 165 + 2.25 = 167.25 2.25 + 3x + x2 = 167.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 167.25 Calculate the square root of the right side: 12.932517156 Break this problem into two subproblems by setting (x + 1.5) equal to 12.932517156 and -12.932517156.Subproblem 1
x + 1.5 = 12.932517156 Simplifying x + 1.5 = 12.932517156 Reorder the terms: 1.5 + x = 12.932517156 Solving 1.5 + x = 12.932517156 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 = 12.932517156 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 12.932517156 + -1.5 x = 12.932517156 + -1.5 Combine like terms: 12.932517156 + -1.5 = 11.432517156 x = 11.432517156 Simplifying x = 11.432517156Subproblem 2
x + 1.5 = -12.932517156 Simplifying x + 1.5 = -12.932517156 Reorder the terms: 1.5 + x = -12.932517156 Solving 1.5 + x = -12.932517156 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 = -12.932517156 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -12.932517156 + -1.5 x = -12.932517156 + -1.5 Combine like terms: -12.932517156 + -1.5 = -14.432517156 x = -14.432517156 Simplifying x = -14.432517156Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.432517156, -14.432517156}
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