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Simplifying x2 + 1.5x + 0.5625 = 0 Reorder the terms: 0.5625 + 1.5x + x2 = 0 Solving 0.5625 + 1.5x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-0.5625' to each side of the equation. 0.5625 + 1.5x + -0.5625 + x2 = 0 + -0.5625 Reorder the terms: 0.5625 + -0.5625 + 1.5x + x2 = 0 + -0.5625 Combine like terms: 0.5625 + -0.5625 = 0.0000 0.0000 + 1.5x + x2 = 0 + -0.5625 1.5x + x2 = 0 + -0.5625 Combine like terms: 0 + -0.5625 = -0.5625 1.5x + x2 = -0.5625 The x term is 1.5x. Take half its coefficient (0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. 1.5x + 0.5625 + x2 = -0.5625 + 0.5625 Reorder the terms: 0.5625 + 1.5x + x2 = -0.5625 + 0.5625 Combine like terms: -0.5625 + 0.5625 = 0.0000 0.5625 + 1.5x + x2 = 0.0000 Factor a perfect square on the left side: (x + 0.75)(x + 0.75) = 0.0000 Calculate the square root of the right side: 0.0000 Break this problem into two subproblems by setting (x + 0.75) equal to 0.0000 and 0.0000.Subproblem 1
x + 0.75 = 0.0000 Simplifying x + 0.75 = 0.0000 Reorder the terms: 0.75 + x = 0.0000 Solving 0.75 + x = 0.0000 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = 0.0000 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = 0.0000 + -0.75 x = 0.0000 + -0.75 Combine like terms: 0.0000 + -0.75 = -0.75 x = -0.75 Simplifying x = -0.75Subproblem 2
x + 0.75 = 0.0000 Simplifying x + 0.75 = 0.0000 Reorder the terms: 0.75 + x = 0.0000 Solving 0.75 + x = 0.0000 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = 0.0000 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = 0.0000 + -0.75 x = 0.0000 + -0.75 Combine like terms: 0.0000 + -0.75 = -0.75 x = -0.75 Simplifying x = -0.75Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.75, -0.75}
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