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Simplifying 0.67x2 + -0.048x + -66.520 = 0 Reorder the terms: -66.520 + -0.048x + 0.67x2 = 0 Solving -66.520 + -0.048x + 0.67x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.67 the coefficient of the squared term: Divide each side by '0.67'. -99.28358209 + -0.07164179104x + x2 = 0 Move the constant term to the right: Add '99.28358209' to each side of the equation. -99.28358209 + -0.07164179104x + 99.28358209 + x2 = 0 + 99.28358209 Reorder the terms: -99.28358209 + 99.28358209 + -0.07164179104x + x2 = 0 + 99.28358209 Combine like terms: -99.28358209 + 99.28358209 = 0.00000000 0.00000000 + -0.07164179104x + x2 = 0 + 99.28358209 -0.07164179104x + x2 = 0 + 99.28358209 Combine like terms: 0 + 99.28358209 = 99.28358209 -0.07164179104x + x2 = 99.28358209 The x term is -0.07164179104x. Take half its coefficient (-0.03582089552). Square it (0.001283136556) and add it to both sides. Add '0.001283136556' to each side of the equation. -0.07164179104x + 0.001283136556 + x2 = 99.28358209 + 0.001283136556 Reorder the terms: 0.001283136556 + -0.07164179104x + x2 = 99.28358209 + 0.001283136556 Combine like terms: 99.28358209 + 0.001283136556 = 99.284865226556 0.001283136556 + -0.07164179104x + x2 = 99.284865226556 Factor a perfect square on the left side: (x + -0.03582089552)(x + -0.03582089552) = 99.284865226556 Calculate the square root of the right side: 9.964179105 Break this problem into two subproblems by setting (x + -0.03582089552) equal to 9.964179105 and -9.964179105.Subproblem 1
x + -0.03582089552 = 9.964179105 Simplifying x + -0.03582089552 = 9.964179105 Reorder the terms: -0.03582089552 + x = 9.964179105 Solving -0.03582089552 + x = 9.964179105 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.03582089552' to each side of the equation. -0.03582089552 + 0.03582089552 + x = 9.964179105 + 0.03582089552 Combine like terms: -0.03582089552 + 0.03582089552 = 0.00000000000 0.00000000000 + x = 9.964179105 + 0.03582089552 x = 9.964179105 + 0.03582089552 Combine like terms: 9.964179105 + 0.03582089552 = 10.00000000052 x = 10.00000000052 Simplifying x = 10.00000000052Subproblem 2
x + -0.03582089552 = -9.964179105 Simplifying x + -0.03582089552 = -9.964179105 Reorder the terms: -0.03582089552 + x = -9.964179105 Solving -0.03582089552 + x = -9.964179105 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.03582089552' to each side of the equation. -0.03582089552 + 0.03582089552 + x = -9.964179105 + 0.03582089552 Combine like terms: -0.03582089552 + 0.03582089552 = 0.00000000000 0.00000000000 + x = -9.964179105 + 0.03582089552 x = -9.964179105 + 0.03582089552 Combine like terms: -9.964179105 + 0.03582089552 = -9.92835820948 x = -9.92835820948 Simplifying x = -9.92835820948Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.00000000052, -9.92835820948}
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