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Simplifying x2 + -1.5x + -20 = 0 Reorder the terms: -20 + -1.5x + x2 = 0 Solving -20 + -1.5x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '20' to each side of the equation. -20 + -1.5x + 20 + x2 = 0 + 20 Reorder the terms: -20 + 20 + -1.5x + x2 = 0 + 20 Combine like terms: -20 + 20 = 0 0 + -1.5x + x2 = 0 + 20 -1.5x + x2 = 0 + 20 Combine like terms: 0 + 20 = 20 -1.5x + x2 = 20 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 = 20 + 0.5625 Reorder the terms: 0.5625 + -1.5x + x2 = 20 + 0.5625 Combine like terms: 20 + 0.5625 = 20.5625 0.5625 + -1.5x + x2 = 20.5625 Factor a perfect square on the left side: (x + -0.75)(x + -0.75) = 20.5625 Calculate the square root of the right side: 4.534589287 Break this problem into two subproblems by setting (x + -0.75) equal to 4.534589287 and -4.534589287.Subproblem 1
x + -0.75 = 4.534589287 Simplifying x + -0.75 = 4.534589287 Reorder the terms: -0.75 + x = 4.534589287 Solving -0.75 + x = 4.534589287 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 = 4.534589287 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = 4.534589287 + 0.75 x = 4.534589287 + 0.75 Combine like terms: 4.534589287 + 0.75 = 5.284589287 x = 5.284589287 Simplifying x = 5.284589287Subproblem 2
x + -0.75 = -4.534589287 Simplifying x + -0.75 = -4.534589287 Reorder the terms: -0.75 + x = -4.534589287 Solving -0.75 + x = -4.534589287 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 = -4.534589287 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = -4.534589287 + 0.75 x = -4.534589287 + 0.75 Combine like terms: -4.534589287 + 0.75 = -3.784589287 x = -3.784589287 Simplifying x = -3.784589287Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.284589287, -3.784589287}
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