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Simplifying -0.01777777778x2 + 1.6x + 15 = 0 Reorder the terms: 15 + 1.6x + -0.01777777778x2 = 0 Solving 15 + 1.6x + -0.01777777778x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.01777777778 the coefficient of the squared term: Divide each side by '-0.01777777778'. -843.7499999 + -89.99999999x + x2 = 0 Move the constant term to the right: Add '843.7499999' to each side of the equation. -843.7499999 + -89.99999999x + 843.7499999 + x2 = 0 + 843.7499999 Reorder the terms: -843.7499999 + 843.7499999 + -89.99999999x + x2 = 0 + 843.7499999 Combine like terms: -843.7499999 + 843.7499999 = 0.0000000 0.0000000 + -89.99999999x + x2 = 0 + 843.7499999 -89.99999999x + x2 = 0 + 843.7499999 Combine like terms: 0 + 843.7499999 = 843.7499999 -89.99999999x + x2 = 843.7499999 The x term is -89.99999999x. Take half its coefficient (-45). Square it (2025) and add it to both sides. Add '2025' to each side of the equation. -89.99999999x + 2025 + x2 = 843.7499999 + 2025 Reorder the terms: 2025 + -89.99999999x + x2 = 843.7499999 + 2025 Combine like terms: 843.7499999 + 2025 = 2868.7499999 2025 + -89.99999999x + x2 = 2868.7499999 Factor a perfect square on the left side: (x + -45)(x + -45) = 2868.7499999 Calculate the square root of the right side: 53.560713213 Break this problem into two subproblems by setting (x + -45) equal to 53.560713213 and -53.560713213.Subproblem 1
x + -45 = 53.560713213 Simplifying x + -45 = 53.560713213 Reorder the terms: -45 + x = 53.560713213 Solving -45 + x = 53.560713213 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '45' to each side of the equation. -45 + 45 + x = 53.560713213 + 45 Combine like terms: -45 + 45 = 0 0 + x = 53.560713213 + 45 x = 53.560713213 + 45 Combine like terms: 53.560713213 + 45 = 98.560713213 x = 98.560713213 Simplifying x = 98.560713213Subproblem 2
x + -45 = -53.560713213 Simplifying x + -45 = -53.560713213 Reorder the terms: -45 + x = -53.560713213 Solving -45 + x = -53.560713213 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '45' to each side of the equation. -45 + 45 + x = -53.560713213 + 45 Combine like terms: -45 + 45 = 0 0 + x = -53.560713213 + 45 x = -53.560713213 + 45 Combine like terms: -53.560713213 + 45 = -8.560713213 x = -8.560713213 Simplifying x = -8.560713213Solution
The solution to the problem is based on the solutions from the subproblems. x = {98.560713213, -8.560713213}
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