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Simplifying 80 = (x)(x + -3) Reorder the terms: 80 = x(-3 + x) 80 = (-3 * x + x * x) 80 = (-3x + x2) Solving 80 = -3x + x2 Solving for variable 'x'. Reorder the terms: 80 + 3x + -1x2 = -3x + 3x + x2 + -1x2 Combine like terms: -3x + 3x = 0 80 + 3x + -1x2 = 0 + x2 + -1x2 80 + 3x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 80 + 3x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -80 + -3x + x2 = 0 Move the constant term to the right: Add '80' to each side of the equation. -80 + -3x + 80 + x2 = 0 + 80 Reorder the terms: -80 + 80 + -3x + x2 = 0 + 80 Combine like terms: -80 + 80 = 0 0 + -3x + x2 = 0 + 80 -3x + x2 = 0 + 80 Combine like terms: 0 + 80 = 80 -3x + x2 = 80 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 = 80 + 2.25 Reorder the terms: 2.25 + -3x + x2 = 80 + 2.25 Combine like terms: 80 + 2.25 = 82.25 2.25 + -3x + x2 = 82.25 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 82.25 Calculate the square root of the right side: 9.069178574 Break this problem into two subproblems by setting (x + -1.5) equal to 9.069178574 and -9.069178574.Subproblem 1
x + -1.5 = 9.069178574 Simplifying x + -1.5 = 9.069178574 Reorder the terms: -1.5 + x = 9.069178574 Solving -1.5 + x = 9.069178574 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 = 9.069178574 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 9.069178574 + 1.5 x = 9.069178574 + 1.5 Combine like terms: 9.069178574 + 1.5 = 10.569178574 x = 10.569178574 Simplifying x = 10.569178574Subproblem 2
x + -1.5 = -9.069178574 Simplifying x + -1.5 = -9.069178574 Reorder the terms: -1.5 + x = -9.069178574 Solving -1.5 + x = -9.069178574 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 = -9.069178574 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -9.069178574 + 1.5 x = -9.069178574 + 1.5 Combine like terms: -9.069178574 + 1.5 = -7.569178574 x = -7.569178574 Simplifying x = -7.569178574Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.569178574, -7.569178574}
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