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Simplifying 5x2 + -28x + -240 = 0 Reorder the terms: -240 + -28x + 5x2 = 0 Solving -240 + -28x + 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 + -5.6x + x2 = 0 Move the constant term to the right: Add '48' to each side of the equation. -48 + -5.6x + 48 + x2 = 0 + 48 Reorder the terms: -48 + 48 + -5.6x + x2 = 0 + 48 Combine like terms: -48 + 48 = 0 0 + -5.6x + x2 = 0 + 48 -5.6x + x2 = 0 + 48 Combine like terms: 0 + 48 = 48 -5.6x + x2 = 48 The x term is -5.6x. Take half its coefficient (-2.8). Square it (7.84) and add it to both sides. Add '7.84' to each side of the equation. -5.6x + 7.84 + x2 = 48 + 7.84 Reorder the terms: 7.84 + -5.6x + x2 = 48 + 7.84 Combine like terms: 48 + 7.84 = 55.84 7.84 + -5.6x + x2 = 55.84 Factor a perfect square on the left side: (x + -2.8)(x + -2.8) = 55.84 Calculate the square root of the right side: 7.472616677 Break this problem into two subproblems by setting (x + -2.8) equal to 7.472616677 and -7.472616677.Subproblem 1
x + -2.8 = 7.472616677 Simplifying x + -2.8 = 7.472616677 Reorder the terms: -2.8 + x = 7.472616677 Solving -2.8 + x = 7.472616677 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.8' to each side of the equation. -2.8 + 2.8 + x = 7.472616677 + 2.8 Combine like terms: -2.8 + 2.8 = 0.0 0.0 + x = 7.472616677 + 2.8 x = 7.472616677 + 2.8 Combine like terms: 7.472616677 + 2.8 = 10.272616677 x = 10.272616677 Simplifying x = 10.272616677Subproblem 2
x + -2.8 = -7.472616677 Simplifying x + -2.8 = -7.472616677 Reorder the terms: -2.8 + x = -7.472616677 Solving -2.8 + x = -7.472616677 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.8' to each side of the equation. -2.8 + 2.8 + x = -7.472616677 + 2.8 Combine like terms: -2.8 + 2.8 = 0.0 0.0 + x = -7.472616677 + 2.8 x = -7.472616677 + 2.8 Combine like terms: -7.472616677 + 2.8 = -4.672616677 x = -4.672616677 Simplifying x = -4.672616677Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.272616677, -4.672616677}
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