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Simplifying x2 + -3.5x + 3 = 0 Reorder the terms: 3 + -3.5x + x2 = 0 Solving 3 + -3.5x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-3' to each side of the equation. 3 + -3.5x + -3 + x2 = 0 + -3 Reorder the terms: 3 + -3 + -3.5x + x2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -3.5x + x2 = 0 + -3 -3.5x + x2 = 0 + -3 Combine like terms: 0 + -3 = -3 -3.5x + x2 = -3 The x term is -3.5x. Take half its coefficient (-1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. -3.5x + 3.0625 + x2 = -3 + 3.0625 Reorder the terms: 3.0625 + -3.5x + x2 = -3 + 3.0625 Combine like terms: -3 + 3.0625 = 0.0625 3.0625 + -3.5x + x2 = 0.0625 Factor a perfect square on the left side: (x + -1.75)(x + -1.75) = 0.0625 Calculate the square root of the right side: 0.25 Break this problem into two subproblems by setting (x + -1.75) equal to 0.25 and -0.25.Subproblem 1
x + -1.75 = 0.25 Simplifying x + -1.75 = 0.25 Reorder the terms: -1.75 + x = 0.25 Solving -1.75 + x = 0.25 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + x = 0.25 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + x = 0.25 + 1.75 x = 0.25 + 1.75 Combine like terms: 0.25 + 1.75 = 2 x = 2 Simplifying x = 2Subproblem 2
x + -1.75 = -0.25 Simplifying x + -1.75 = -0.25 Reorder the terms: -1.75 + x = -0.25 Solving -1.75 + x = -0.25 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + x = -0.25 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + x = -0.25 + 1.75 x = -0.25 + 1.75 Combine like terms: -0.25 + 1.75 = 1.5 x = 1.5 Simplifying x = 1.5Solution
The solution to the problem is based on the solutions from the subproblems. x = {2, 1.5}
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