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Simplifying 5x2 + -5x + -56 = 0 Reorder the terms: -56 + -5x + 5x2 = 0 Solving -56 + -5x + 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'. -11.2 + -1x + x2 = 0 Move the constant term to the right: Add '11.2' to each side of the equation. -11.2 + -1x + 11.2 + x2 = 0 + 11.2 Reorder the terms: -11.2 + 11.2 + -1x + x2 = 0 + 11.2 Combine like terms: -11.2 + 11.2 = 0.0 0.0 + -1x + x2 = 0 + 11.2 -1x + x2 = 0 + 11.2 Combine like terms: 0 + 11.2 = 11.2 -1x + x2 = 11.2 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = 11.2 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 11.2 + 0.25 Combine like terms: 11.2 + 0.25 = 11.45 0.25 + -1x + x2 = 11.45 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 11.45 Calculate the square root of the right side: 3.383784863 Break this problem into two subproblems by setting (x + -0.5) equal to 3.383784863 and -3.383784863.Subproblem 1
x + -0.5 = 3.383784863 Simplifying x + -0.5 = 3.383784863 Reorder the terms: -0.5 + x = 3.383784863 Solving -0.5 + x = 3.383784863 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 3.383784863 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 3.383784863 + 0.5 x = 3.383784863 + 0.5 Combine like terms: 3.383784863 + 0.5 = 3.883784863 x = 3.883784863 Simplifying x = 3.883784863Subproblem 2
x + -0.5 = -3.383784863 Simplifying x + -0.5 = -3.383784863 Reorder the terms: -0.5 + x = -3.383784863 Solving -0.5 + x = -3.383784863 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -3.383784863 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -3.383784863 + 0.5 x = -3.383784863 + 0.5 Combine like terms: -3.383784863 + 0.5 = -2.883784863 x = -2.883784863 Simplifying x = -2.883784863Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.883784863, -2.883784863}
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