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Simplifying x2 + -1.5x + -4.5 = 0 Reorder the terms: -4.5 + -1.5x + x2 = 0 Solving -4.5 + -1.5x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '4.5' to each side of the equation. -4.5 + -1.5x + 4.5 + x2 = 0 + 4.5 Reorder the terms: -4.5 + 4.5 + -1.5x + x2 = 0 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + -1.5x + x2 = 0 + 4.5 -1.5x + x2 = 0 + 4.5 Combine like terms: 0 + 4.5 = 4.5 -1.5x + x2 = 4.5 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 = 4.5 + 0.5625 Reorder the terms: 0.5625 + -1.5x + x2 = 4.5 + 0.5625 Combine like terms: 4.5 + 0.5625 = 5.0625 0.5625 + -1.5x + x2 = 5.0625 Factor a perfect square on the left side: (x + -0.75)(x + -0.75) = 5.0625 Calculate the square root of the right side: 2.25 Break this problem into two subproblems by setting (x + -0.75) equal to 2.25 and -2.25.Subproblem 1
x + -0.75 = 2.25 Simplifying x + -0.75 = 2.25 Reorder the terms: -0.75 + x = 2.25 Solving -0.75 + x = 2.25 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 = 2.25 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = 2.25 + 0.75 x = 2.25 + 0.75 Combine like terms: 2.25 + 0.75 = 3 x = 3 Simplifying x = 3Subproblem 2
x + -0.75 = -2.25 Simplifying x + -0.75 = -2.25 Reorder the terms: -0.75 + x = -2.25 Solving -0.75 + x = -2.25 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 = -2.25 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = -2.25 + 0.75 x = -2.25 + 0.75 Combine like terms: -2.25 + 0.75 = -1.5 x = -1.5 Simplifying x = -1.5Solution
The solution to the problem is based on the solutions from the subproblems. x = {3, -1.5}
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