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Simplifying x2 + -2.45x + 1.5 = 0 Reorder the terms: 1.5 + -2.45x + x2 = 0 Solving 1.5 + -2.45x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-1.5' to each side of the equation. 1.5 + -2.45x + -1.5 + x2 = 0 + -1.5 Reorder the terms: 1.5 + -1.5 + -2.45x + x2 = 0 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + -2.45x + x2 = 0 + -1.5 -2.45x + x2 = 0 + -1.5 Combine like terms: 0 + -1.5 = -1.5 -2.45x + x2 = -1.5 The x term is -2.45x. Take half its coefficient (-1.225). Square it (1.500625) and add it to both sides. Add '1.500625' to each side of the equation. -2.45x + 1.500625 + x2 = -1.5 + 1.500625 Reorder the terms: 1.500625 + -2.45x + x2 = -1.5 + 1.500625 Combine like terms: -1.5 + 1.500625 = 0.000625 1.500625 + -2.45x + x2 = 0.000625 Factor a perfect square on the left side: (x + -1.225)(x + -1.225) = 0.000625 Calculate the square root of the right side: 0.025 Break this problem into two subproblems by setting (x + -1.225) equal to 0.025 and -0.025.Subproblem 1
x + -1.225 = 0.025 Simplifying x + -1.225 = 0.025 Reorder the terms: -1.225 + x = 0.025 Solving -1.225 + x = 0.025 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.225' to each side of the equation. -1.225 + 1.225 + x = 0.025 + 1.225 Combine like terms: -1.225 + 1.225 = 0.000 0.000 + x = 0.025 + 1.225 x = 0.025 + 1.225 Combine like terms: 0.025 + 1.225 = 1.25 x = 1.25 Simplifying x = 1.25Subproblem 2
x + -1.225 = -0.025 Simplifying x + -1.225 = -0.025 Reorder the terms: -1.225 + x = -0.025 Solving -1.225 + x = -0.025 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.225' to each side of the equation. -1.225 + 1.225 + x = -0.025 + 1.225 Combine like terms: -1.225 + 1.225 = 0.000 0.000 + x = -0.025 + 1.225 x = -0.025 + 1.225 Combine like terms: -0.025 + 1.225 = 1.2 x = 1.2 Simplifying x = 1.2Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.25, 1.2}
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