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Simplifying 130 = -80x2 + 440x + 0 Reorder the terms: 130 = 0 + 440x + -80x2 Remove the zero: 130 = 440x + -80x2 Solving 130 = 440x + -80x2 Solving for variable 'x'. Reorder the terms: 130 + -440x + 80x2 = 440x + -440x + -80x2 + 80x2 Combine like terms: 440x + -440x = 0 130 + -440x + 80x2 = 0 + -80x2 + 80x2 130 + -440x + 80x2 = -80x2 + 80x2 Combine like terms: -80x2 + 80x2 = 0 130 + -440x + 80x2 = 0 Factor out the Greatest Common Factor (GCF), '10'. 10(13 + -44x + 8x2) = 0 Ignore the factor 10.Subproblem 1
Set the factor '(13 + -44x + 8x2)' equal to zero and attempt to solve: Simplifying 13 + -44x + 8x2 = 0 Solving 13 + -44x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 1.625 + -5.5x + x2 = 0 Move the constant term to the right: Add '-1.625' to each side of the equation. 1.625 + -5.5x + -1.625 + x2 = 0 + -1.625 Reorder the terms: 1.625 + -1.625 + -5.5x + x2 = 0 + -1.625 Combine like terms: 1.625 + -1.625 = 0.000 0.000 + -5.5x + x2 = 0 + -1.625 -5.5x + x2 = 0 + -1.625 Combine like terms: 0 + -1.625 = -1.625 -5.5x + x2 = -1.625 The x term is -5.5x. Take half its coefficient (-2.75). Square it (7.5625) and add it to both sides. Add '7.5625' to each side of the equation. -5.5x + 7.5625 + x2 = -1.625 + 7.5625 Reorder the terms: 7.5625 + -5.5x + x2 = -1.625 + 7.5625 Combine like terms: -1.625 + 7.5625 = 5.9375 7.5625 + -5.5x + x2 = 5.9375 Factor a perfect square on the left side: (x + -2.75)(x + -2.75) = 5.9375 Calculate the square root of the right side: 2.436698586 Break this problem into two subproblems by setting (x + -2.75) equal to 2.436698586 and -2.436698586.Subproblem 1
x + -2.75 = 2.436698586 Simplifying x + -2.75 = 2.436698586 Reorder the terms: -2.75 + x = 2.436698586 Solving -2.75 + x = 2.436698586 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.75' to each side of the equation. -2.75 + 2.75 + x = 2.436698586 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + x = 2.436698586 + 2.75 x = 2.436698586 + 2.75 Combine like terms: 2.436698586 + 2.75 = 5.186698586 x = 5.186698586 Simplifying x = 5.186698586Subproblem 2
x + -2.75 = -2.436698586 Simplifying x + -2.75 = -2.436698586 Reorder the terms: -2.75 + x = -2.436698586 Solving -2.75 + x = -2.436698586 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.75' to each side of the equation. -2.75 + 2.75 + x = -2.436698586 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + x = -2.436698586 + 2.75 x = -2.436698586 + 2.75 Combine like terms: -2.436698586 + 2.75 = 0.313301414 x = 0.313301414 Simplifying x = 0.313301414Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.186698586, 0.313301414}Solution
x = {5.186698586, 0.313301414}
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