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Simplifying 7x + 13 + -5x2 + 8x = 0 Reorder the terms: 13 + 7x + 8x + -5x2 = 0 Combine like terms: 7x + 8x = 15x 13 + 15x + -5x2 = 0 Solving 13 + 15x + -5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -2.6 + -3x + x2 = 0 Move the constant term to the right: Add '2.6' to each side of the equation. -2.6 + -3x + 2.6 + x2 = 0 + 2.6 Reorder the terms: -2.6 + 2.6 + -3x + x2 = 0 + 2.6 Combine like terms: -2.6 + 2.6 = 0.0 0.0 + -3x + x2 = 0 + 2.6 -3x + x2 = 0 + 2.6 Combine like terms: 0 + 2.6 = 2.6 -3x + x2 = 2.6 The x term is -3x. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3x + 2.25 + x2 = 2.6 + 2.25 Reorder the terms: 2.25 + -3x + x2 = 2.6 + 2.25 Combine like terms: 2.6 + 2.25 = 4.85 2.25 + -3x + x2 = 4.85 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 4.85 Calculate the square root of the right side: 2.202271555 Break this problem into two subproblems by setting (x + -1.5) equal to 2.202271555 and -2.202271555.Subproblem 1
x + -1.5 = 2.202271555 Simplifying x + -1.5 = 2.202271555 Reorder the terms: -1.5 + x = 2.202271555 Solving -1.5 + x = 2.202271555 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = 2.202271555 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 2.202271555 + 1.5 x = 2.202271555 + 1.5 Combine like terms: 2.202271555 + 1.5 = 3.702271555 x = 3.702271555 Simplifying x = 3.702271555Subproblem 2
x + -1.5 = -2.202271555 Simplifying x + -1.5 = -2.202271555 Reorder the terms: -1.5 + x = -2.202271555 Solving -1.5 + x = -2.202271555 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = -2.202271555 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -2.202271555 + 1.5 x = -2.202271555 + 1.5 Combine like terms: -2.202271555 + 1.5 = -0.702271555 x = -0.702271555 Simplifying x = -0.702271555Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.702271555, -0.702271555}
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