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Simplifying -16x2 + 40x + 80 = 104.64 Reorder the terms: 80 + 40x + -16x2 = 104.64 Solving 80 + 40x + -16x2 = 104.64 Solving for variable 'x'. Reorder the terms: 80 + -104.64 + 40x + -16x2 = 104.64 + -104.64 Combine like terms: 80 + -104.64 = -24.64 -24.64 + 40x + -16x2 = 104.64 + -104.64 Combine like terms: 104.64 + -104.64 = 0.00 -24.64 + 40x + -16x2 = 0.00 Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. 1.54 + -2.5x + x2 = 0.00 Move the constant term to the right: Add '-1.54' to each side of the equation. 1.54 + -2.5x + -1.54 + x2 = 0.00 + -1.54 Reorder the terms: 1.54 + -1.54 + -2.5x + x2 = 0.00 + -1.54 Combine like terms: 1.54 + -1.54 = 0.00 0.00 + -2.5x + x2 = 0.00 + -1.54 -2.5x + x2 = 0.00 + -1.54 Combine like terms: 0.00 + -1.54 = -1.54 -2.5x + x2 = -1.54 The x term is -2.5x. Take half its coefficient (-1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. -2.5x + 1.5625 + x2 = -1.54 + 1.5625 Reorder the terms: 1.5625 + -2.5x + x2 = -1.54 + 1.5625 Combine like terms: -1.54 + 1.5625 = 0.0225 1.5625 + -2.5x + x2 = 0.0225 Factor a perfect square on the left side: (x + -1.25)(x + -1.25) = 0.0225 Calculate the square root of the right side: 0.15 Break this problem into two subproblems by setting (x + -1.25) equal to 0.15 and -0.15.Subproblem 1
x + -1.25 = 0.15 Simplifying x + -1.25 = 0.15 Reorder the terms: -1.25 + x = 0.15 Solving -1.25 + x = 0.15 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = 0.15 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = 0.15 + 1.25 x = 0.15 + 1.25 Combine like terms: 0.15 + 1.25 = 1.4 x = 1.4 Simplifying x = 1.4Subproblem 2
x + -1.25 = -0.15 Simplifying x + -1.25 = -0.15 Reorder the terms: -1.25 + x = -0.15 Solving -1.25 + x = -0.15 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = -0.15 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = -0.15 + 1.25 x = -0.15 + 1.25 Combine like terms: -0.15 + 1.25 = 1.1 x = 1.1 Simplifying x = 1.1Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.4, 1.1}
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