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Simplifying -2.5x2 + -48x + 40 = 0 Reorder the terms: 40 + -48x + -2.5x2 = 0 Solving 40 + -48x + -2.5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -2.5 the coefficient of the squared term: Divide each side by '-2.5'. -16 + 19.2x + x2 = 0 Move the constant term to the right: Add '16' to each side of the equation. -16 + 19.2x + 16 + x2 = 0 + 16 Reorder the terms: -16 + 16 + 19.2x + x2 = 0 + 16 Combine like terms: -16 + 16 = 0 0 + 19.2x + x2 = 0 + 16 19.2x + x2 = 0 + 16 Combine like terms: 0 + 16 = 16 19.2x + x2 = 16 The x term is 19.2x. Take half its coefficient (9.6). Square it (92.16) and add it to both sides. Add '92.16' to each side of the equation. 19.2x + 92.16 + x2 = 16 + 92.16 Reorder the terms: 92.16 + 19.2x + x2 = 16 + 92.16 Combine like terms: 16 + 92.16 = 108.16 92.16 + 19.2x + x2 = 108.16 Factor a perfect square on the left side: (x + 9.6)(x + 9.6) = 108.16 Calculate the square root of the right side: 10.4 Break this problem into two subproblems by setting (x + 9.6) equal to 10.4 and -10.4.Subproblem 1
x + 9.6 = 10.4 Simplifying x + 9.6 = 10.4 Reorder the terms: 9.6 + x = 10.4 Solving 9.6 + x = 10.4 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9.6' to each side of the equation. 9.6 + -9.6 + x = 10.4 + -9.6 Combine like terms: 9.6 + -9.6 = 0.0 0.0 + x = 10.4 + -9.6 x = 10.4 + -9.6 Combine like terms: 10.4 + -9.6 = 0.8 x = 0.8 Simplifying x = 0.8Subproblem 2
x + 9.6 = -10.4 Simplifying x + 9.6 = -10.4 Reorder the terms: 9.6 + x = -10.4 Solving 9.6 + x = -10.4 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9.6' to each side of the equation. 9.6 + -9.6 + x = -10.4 + -9.6 Combine like terms: 9.6 + -9.6 = 0.0 0.0 + x = -10.4 + -9.6 x = -10.4 + -9.6 Combine like terms: -10.4 + -9.6 = -20 x = -20 Simplifying x = -20Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.8, -20}
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