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Simplifying x2 + 3x = 145 Reorder the terms: 3x + x2 = 145 Solving 3x + x2 = 145 Solving for variable 'x'. Reorder the terms: -145 + 3x + x2 = 145 + -145 Combine like terms: 145 + -145 = 0 -145 + 3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '145' to each side of the equation. -145 + 3x + 145 + x2 = 0 + 145 Reorder the terms: -145 + 145 + 3x + x2 = 0 + 145 Combine like terms: -145 + 145 = 0 0 + 3x + x2 = 0 + 145 3x + x2 = 0 + 145 Combine like terms: 0 + 145 = 145 3x + x2 = 145 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 = 145 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 145 + 2.25 Combine like terms: 145 + 2.25 = 147.25 2.25 + 3x + x2 = 147.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 147.25 Calculate the square root of the right side: 12.1346611 Break this problem into two subproblems by setting (x + 1.5) equal to 12.1346611 and -12.1346611.Subproblem 1
x + 1.5 = 12.1346611 Simplifying x + 1.5 = 12.1346611 Reorder the terms: 1.5 + x = 12.1346611 Solving 1.5 + x = 12.1346611 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 = 12.1346611 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 12.1346611 + -1.5 x = 12.1346611 + -1.5 Combine like terms: 12.1346611 + -1.5 = 10.6346611 x = 10.6346611 Simplifying x = 10.6346611Subproblem 2
x + 1.5 = -12.1346611 Simplifying x + 1.5 = -12.1346611 Reorder the terms: 1.5 + x = -12.1346611 Solving 1.5 + x = -12.1346611 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 = -12.1346611 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -12.1346611 + -1.5 x = -12.1346611 + -1.5 Combine like terms: -12.1346611 + -1.5 = -13.6346611 x = -13.6346611 Simplifying x = -13.6346611Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.6346611, -13.6346611}
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