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Simplifying x2 + 3x + -0.45 = 0 Reorder the terms: -0.45 + 3x + x2 = 0 Solving -0.45 + 3x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '0.45' to each side of the equation. -0.45 + 3x + 0.45 + x2 = 0 + 0.45 Reorder the terms: -0.45 + 0.45 + 3x + x2 = 0 + 0.45 Combine like terms: -0.45 + 0.45 = 0.00 0.00 + 3x + x2 = 0 + 0.45 3x + x2 = 0 + 0.45 Combine like terms: 0 + 0.45 = 0.45 3x + x2 = 0.45 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 = 0.45 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 0.45 + 2.25 Combine like terms: 0.45 + 2.25 = 2.7 2.25 + 3x + x2 = 2.7 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 2.7 Calculate the square root of the right side: 1.643167673 Break this problem into two subproblems by setting (x + 1.5) equal to 1.643167673 and -1.643167673.Subproblem 1
x + 1.5 = 1.643167673 Simplifying x + 1.5 = 1.643167673 Reorder the terms: 1.5 + x = 1.643167673 Solving 1.5 + x = 1.643167673 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 = 1.643167673 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 1.643167673 + -1.5 x = 1.643167673 + -1.5 Combine like terms: 1.643167673 + -1.5 = 0.143167673 x = 0.143167673 Simplifying x = 0.143167673Subproblem 2
x + 1.5 = -1.643167673 Simplifying x + 1.5 = -1.643167673 Reorder the terms: 1.5 + x = -1.643167673 Solving 1.5 + x = -1.643167673 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 = -1.643167673 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -1.643167673 + -1.5 x = -1.643167673 + -1.5 Combine like terms: -1.643167673 + -1.5 = -3.143167673 x = -3.143167673 Simplifying x = -3.143167673Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.143167673, -3.143167673}
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