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Simplifying 160 = x(x + 3) Reorder the terms: 160 = x(3 + x) 160 = (3 * x + x * x) 160 = (3x + x2) Solving 160 = 3x + x2 Solving for variable 'x'. Reorder the terms: 160 + -3x + -1x2 = 3x + -3x + x2 + -1x2 Combine like terms: 3x + -3x = 0 160 + -3x + -1x2 = 0 + x2 + -1x2 160 + -3x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 160 + -3x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -160 + 3x + x2 = 0 Move the constant term to the right: Add '160' to each side of the equation. -160 + 3x + 160 + x2 = 0 + 160 Reorder the terms: -160 + 160 + 3x + x2 = 0 + 160 Combine like terms: -160 + 160 = 0 0 + 3x + x2 = 0 + 160 3x + x2 = 0 + 160 Combine like terms: 0 + 160 = 160 3x + x2 = 160 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 = 160 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 160 + 2.25 Combine like terms: 160 + 2.25 = 162.25 2.25 + 3x + x2 = 162.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 162.25 Calculate the square root of the right side: 12.737739203 Break this problem into two subproblems by setting (x + 1.5) equal to 12.737739203 and -12.737739203.Subproblem 1
x + 1.5 = 12.737739203 Simplifying x + 1.5 = 12.737739203 Reorder the terms: 1.5 + x = 12.737739203 Solving 1.5 + x = 12.737739203 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 = 12.737739203 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 12.737739203 + -1.5 x = 12.737739203 + -1.5 Combine like terms: 12.737739203 + -1.5 = 11.237739203 x = 11.237739203 Simplifying x = 11.237739203Subproblem 2
x + 1.5 = -12.737739203 Simplifying x + 1.5 = -12.737739203 Reorder the terms: 1.5 + x = -12.737739203 Solving 1.5 + x = -12.737739203 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 = -12.737739203 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -12.737739203 + -1.5 x = -12.737739203 + -1.5 Combine like terms: -12.737739203 + -1.5 = -14.237739203 x = -14.237739203 Simplifying x = -14.237739203Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.237739203, -14.237739203}
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