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Simplifying x2 + -8.5x + 3 = 0 Reorder the terms: 3 + -8.5x + x2 = 0 Solving 3 + -8.5x + 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 + -8.5x + -3 + x2 = 0 + -3 Reorder the terms: 3 + -3 + -8.5x + x2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -8.5x + x2 = 0 + -3 -8.5x + x2 = 0 + -3 Combine like terms: 0 + -3 = -3 -8.5x + x2 = -3 The x term is -8.5x. Take half its coefficient (-4.25). Square it (18.0625) and add it to both sides. Add '18.0625' to each side of the equation. -8.5x + 18.0625 + x2 = -3 + 18.0625 Reorder the terms: 18.0625 + -8.5x + x2 = -3 + 18.0625 Combine like terms: -3 + 18.0625 = 15.0625 18.0625 + -8.5x + x2 = 15.0625 Factor a perfect square on the left side: (x + -4.25)(x + -4.25) = 15.0625 Calculate the square root of the right side: 3.881043674 Break this problem into two subproblems by setting (x + -4.25) equal to 3.881043674 and -3.881043674.Subproblem 1
x + -4.25 = 3.881043674 Simplifying x + -4.25 = 3.881043674 Reorder the terms: -4.25 + x = 3.881043674 Solving -4.25 + x = 3.881043674 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.25' to each side of the equation. -4.25 + 4.25 + x = 3.881043674 + 4.25 Combine like terms: -4.25 + 4.25 = 0.00 0.00 + x = 3.881043674 + 4.25 x = 3.881043674 + 4.25 Combine like terms: 3.881043674 + 4.25 = 8.131043674 x = 8.131043674 Simplifying x = 8.131043674Subproblem 2
x + -4.25 = -3.881043674 Simplifying x + -4.25 = -3.881043674 Reorder the terms: -4.25 + x = -3.881043674 Solving -4.25 + x = -3.881043674 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.25' to each side of the equation. -4.25 + 4.25 + x = -3.881043674 + 4.25 Combine like terms: -4.25 + 4.25 = 0.00 0.00 + x = -3.881043674 + 4.25 x = -3.881043674 + 4.25 Combine like terms: -3.881043674 + 4.25 = 0.368956326 x = 0.368956326 Simplifying x = 0.368956326Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.131043674, 0.368956326}
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