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Simplifying 5x2 + 52x + -48 = 0 Reorder the terms: -48 + 52x + 5x2 = 0 Solving -48 + 52x + 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'. -9.6 + 10.4x + x2 = 0 Move the constant term to the right: Add '9.6' to each side of the equation. -9.6 + 10.4x + 9.6 + x2 = 0 + 9.6 Reorder the terms: -9.6 + 9.6 + 10.4x + x2 = 0 + 9.6 Combine like terms: -9.6 + 9.6 = 0.0 0.0 + 10.4x + x2 = 0 + 9.6 10.4x + x2 = 0 + 9.6 Combine like terms: 0 + 9.6 = 9.6 10.4x + x2 = 9.6 The x term is 10.4x. Take half its coefficient (5.2). Square it (27.04) and add it to both sides. Add '27.04' to each side of the equation. 10.4x + 27.04 + x2 = 9.6 + 27.04 Reorder the terms: 27.04 + 10.4x + x2 = 9.6 + 27.04 Combine like terms: 9.6 + 27.04 = 36.64 27.04 + 10.4x + x2 = 36.64 Factor a perfect square on the left side: (x + 5.2)(x + 5.2) = 36.64 Calculate the square root of the right side: 6.05309838 Break this problem into two subproblems by setting (x + 5.2) equal to 6.05309838 and -6.05309838.Subproblem 1
x + 5.2 = 6.05309838 Simplifying x + 5.2 = 6.05309838 Reorder the terms: 5.2 + x = 6.05309838 Solving 5.2 + x = 6.05309838 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.2' to each side of the equation. 5.2 + -5.2 + x = 6.05309838 + -5.2 Combine like terms: 5.2 + -5.2 = 0.0 0.0 + x = 6.05309838 + -5.2 x = 6.05309838 + -5.2 Combine like terms: 6.05309838 + -5.2 = 0.85309838 x = 0.85309838 Simplifying x = 0.85309838Subproblem 2
x + 5.2 = -6.05309838 Simplifying x + 5.2 = -6.05309838 Reorder the terms: 5.2 + x = -6.05309838 Solving 5.2 + x = -6.05309838 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.2' to each side of the equation. 5.2 + -5.2 + x = -6.05309838 + -5.2 Combine like terms: 5.2 + -5.2 = 0.0 0.0 + x = -6.05309838 + -5.2 x = -6.05309838 + -5.2 Combine like terms: -6.05309838 + -5.2 = -11.25309838 x = -11.25309838 Simplifying x = -11.25309838Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.85309838, -11.25309838}
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