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Simplifying x2 + -1.5x + -0.35 = 0 Reorder the terms: -0.35 + -1.5x + x2 = 0 Solving -0.35 + -1.5x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '0.35' to each side of the equation. -0.35 + -1.5x + 0.35 + x2 = 0 + 0.35 Reorder the terms: -0.35 + 0.35 + -1.5x + x2 = 0 + 0.35 Combine like terms: -0.35 + 0.35 = 0.00 0.00 + -1.5x + x2 = 0 + 0.35 -1.5x + x2 = 0 + 0.35 Combine like terms: 0 + 0.35 = 0.35 -1.5x + x2 = 0.35 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 = 0.35 + 0.5625 Reorder the terms: 0.5625 + -1.5x + x2 = 0.35 + 0.5625 Combine like terms: 0.35 + 0.5625 = 0.9125 0.5625 + -1.5x + x2 = 0.9125 Factor a perfect square on the left side: (x + -0.75)(x + -0.75) = 0.9125 Calculate the square root of the right side: 0.955248659 Break this problem into two subproblems by setting (x + -0.75) equal to 0.955248659 and -0.955248659.Subproblem 1
x + -0.75 = 0.955248659 Simplifying x + -0.75 = 0.955248659 Reorder the terms: -0.75 + x = 0.955248659 Solving -0.75 + x = 0.955248659 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 = 0.955248659 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = 0.955248659 + 0.75 x = 0.955248659 + 0.75 Combine like terms: 0.955248659 + 0.75 = 1.705248659 x = 1.705248659 Simplifying x = 1.705248659Subproblem 2
x + -0.75 = -0.955248659 Simplifying x + -0.75 = -0.955248659 Reorder the terms: -0.75 + x = -0.955248659 Solving -0.75 + x = -0.955248659 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 = -0.955248659 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = -0.955248659 + 0.75 x = -0.955248659 + 0.75 Combine like terms: -0.955248659 + 0.75 = -0.205248659 x = -0.205248659 Simplifying x = -0.205248659Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.705248659, -0.205248659}
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