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Simplifying 0.25x2 + 1.5x + -6.5 = 0 Reorder the terms: -6.5 + 1.5x + 0.25x2 = 0 Solving -6.5 + 1.5x + 0.25x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.25 the coefficient of the squared term: Divide each side by '0.25'. -26 + 6x + x2 = 0 Move the constant term to the right: Add '26' to each side of the equation. -26 + 6x + 26 + x2 = 0 + 26 Reorder the terms: -26 + 26 + 6x + x2 = 0 + 26 Combine like terms: -26 + 26 = 0 0 + 6x + x2 = 0 + 26 6x + x2 = 0 + 26 Combine like terms: 0 + 26 = 26 6x + x2 = 26 The x term is 6x. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x + 9 + x2 = 26 + 9 Reorder the terms: 9 + 6x + x2 = 26 + 9 Combine like terms: 26 + 9 = 35 9 + 6x + x2 = 35 Factor a perfect square on the left side: (x + 3)(x + 3) = 35 Calculate the square root of the right side: 5.916079783 Break this problem into two subproblems by setting (x + 3) equal to 5.916079783 and -5.916079783.Subproblem 1
x + 3 = 5.916079783 Simplifying x + 3 = 5.916079783 Reorder the terms: 3 + x = 5.916079783 Solving 3 + x = 5.916079783 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 5.916079783 + -3 Combine like terms: 3 + -3 = 0 0 + x = 5.916079783 + -3 x = 5.916079783 + -3 Combine like terms: 5.916079783 + -3 = 2.916079783 x = 2.916079783 Simplifying x = 2.916079783Subproblem 2
x + 3 = -5.916079783 Simplifying x + 3 = -5.916079783 Reorder the terms: 3 + x = -5.916079783 Solving 3 + x = -5.916079783 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -5.916079783 + -3 Combine like terms: 3 + -3 = 0 0 + x = -5.916079783 + -3 x = -5.916079783 + -3 Combine like terms: -5.916079783 + -3 = -8.916079783 x = -8.916079783 Simplifying x = -8.916079783Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.916079783, -8.916079783}
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