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Simplifying 5x2 + 92x + -240 = 0 Reorder the terms: -240 + 92x + 5x2 = 0 Solving -240 + 92x + 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'. -48 + 18.4x + x2 = 0 Move the constant term to the right: Add '48' to each side of the equation. -48 + 18.4x + 48 + x2 = 0 + 48 Reorder the terms: -48 + 48 + 18.4x + x2 = 0 + 48 Combine like terms: -48 + 48 = 0 0 + 18.4x + x2 = 0 + 48 18.4x + x2 = 0 + 48 Combine like terms: 0 + 48 = 48 18.4x + x2 = 48 The x term is 18.4x. Take half its coefficient (9.2). Square it (84.64) and add it to both sides. Add '84.64' to each side of the equation. 18.4x + 84.64 + x2 = 48 + 84.64 Reorder the terms: 84.64 + 18.4x + x2 = 48 + 84.64 Combine like terms: 48 + 84.64 = 132.64 84.64 + 18.4x + x2 = 132.64 Factor a perfect square on the left side: (x + 9.2)(x + 9.2) = 132.64 Calculate the square root of the right side: 11.516944039 Break this problem into two subproblems by setting (x + 9.2) equal to 11.516944039 and -11.516944039.Subproblem 1
x + 9.2 = 11.516944039 Simplifying x + 9.2 = 11.516944039 Reorder the terms: 9.2 + x = 11.516944039 Solving 9.2 + x = 11.516944039 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9.2' to each side of the equation. 9.2 + -9.2 + x = 11.516944039 + -9.2 Combine like terms: 9.2 + -9.2 = 0.0 0.0 + x = 11.516944039 + -9.2 x = 11.516944039 + -9.2 Combine like terms: 11.516944039 + -9.2 = 2.316944039 x = 2.316944039 Simplifying x = 2.316944039Subproblem 2
x + 9.2 = -11.516944039 Simplifying x + 9.2 = -11.516944039 Reorder the terms: 9.2 + x = -11.516944039 Solving 9.2 + x = -11.516944039 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9.2' to each side of the equation. 9.2 + -9.2 + x = -11.516944039 + -9.2 Combine like terms: 9.2 + -9.2 = 0.0 0.0 + x = -11.516944039 + -9.2 x = -11.516944039 + -9.2 Combine like terms: -11.516944039 + -9.2 = -20.716944039 x = -20.716944039 Simplifying x = -20.716944039Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.316944039, -20.716944039}
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