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Simplifying x2 + 3x + -147 = 0 Reorder the terms: -147 + 3x + x2 = 0 Solving -147 + 3x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '147' to each side of the equation. -147 + 3x + 147 + x2 = 0 + 147 Reorder the terms: -147 + 147 + 3x + x2 = 0 + 147 Combine like terms: -147 + 147 = 0 0 + 3x + x2 = 0 + 147 3x + x2 = 0 + 147 Combine like terms: 0 + 147 = 147 3x + x2 = 147 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 = 147 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 147 + 2.25 Combine like terms: 147 + 2.25 = 149.25 2.25 + 3x + x2 = 149.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 149.25 Calculate the square root of the right side: 12.216791723 Break this problem into two subproblems by setting (x + 1.5) equal to 12.216791723 and -12.216791723.Subproblem 1
x + 1.5 = 12.216791723 Simplifying x + 1.5 = 12.216791723 Reorder the terms: 1.5 + x = 12.216791723 Solving 1.5 + x = 12.216791723 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 = 12.216791723 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 12.216791723 + -1.5 x = 12.216791723 + -1.5 Combine like terms: 12.216791723 + -1.5 = 10.716791723 x = 10.716791723 Simplifying x = 10.716791723Subproblem 2
x + 1.5 = -12.216791723 Simplifying x + 1.5 = -12.216791723 Reorder the terms: 1.5 + x = -12.216791723 Solving 1.5 + x = -12.216791723 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 = -12.216791723 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -12.216791723 + -1.5 x = -12.216791723 + -1.5 Combine like terms: -12.216791723 + -1.5 = -13.716791723 x = -13.716791723 Simplifying x = -13.716791723Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.716791723, -13.716791723}
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