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Simplifying 6.5x = x2 + -10 Reorder the terms: 6.5x = -10 + x2 Solving 6.5x = -10 + x2 Solving for variable 'x'. Reorder the terms: 10 + 6.5x + -1x2 = -10 + x2 + 10 + -1x2 Reorder the terms: 10 + 6.5x + -1x2 = -10 + 10 + x2 + -1x2 Combine like terms: -10 + 10 = 0 10 + 6.5x + -1x2 = 0 + x2 + -1x2 10 + 6.5x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 10 + 6.5x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -10 + -6.5x + x2 = 0 Move the constant term to the right: Add '10' to each side of the equation. -10 + -6.5x + 10 + x2 = 0 + 10 Reorder the terms: -10 + 10 + -6.5x + x2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + -6.5x + x2 = 0 + 10 -6.5x + x2 = 0 + 10 Combine like terms: 0 + 10 = 10 -6.5x + x2 = 10 The x term is -6.5x. Take half its coefficient (-3.25). Square it (10.5625) and add it to both sides. Add '10.5625' to each side of the equation. -6.5x + 10.5625 + x2 = 10 + 10.5625 Reorder the terms: 10.5625 + -6.5x + x2 = 10 + 10.5625 Combine like terms: 10 + 10.5625 = 20.5625 10.5625 + -6.5x + x2 = 20.5625 Factor a perfect square on the left side: (x + -3.25)(x + -3.25) = 20.5625 Calculate the square root of the right side: 4.534589287 Break this problem into two subproblems by setting (x + -3.25) equal to 4.534589287 and -4.534589287.Subproblem 1
x + -3.25 = 4.534589287 Simplifying x + -3.25 = 4.534589287 Reorder the terms: -3.25 + x = 4.534589287 Solving -3.25 + x = 4.534589287 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.25' to each side of the equation. -3.25 + 3.25 + x = 4.534589287 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + x = 4.534589287 + 3.25 x = 4.534589287 + 3.25 Combine like terms: 4.534589287 + 3.25 = 7.784589287 x = 7.784589287 Simplifying x = 7.784589287Subproblem 2
x + -3.25 = -4.534589287 Simplifying x + -3.25 = -4.534589287 Reorder the terms: -3.25 + x = -4.534589287 Solving -3.25 + x = -4.534589287 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.25' to each side of the equation. -3.25 + 3.25 + x = -4.534589287 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + x = -4.534589287 + 3.25 x = -4.534589287 + 3.25 Combine like terms: -4.534589287 + 3.25 = -1.284589287 x = -1.284589287 Simplifying x = -1.284589287Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.784589287, -1.284589287}
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