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Simplifying 49.3x2 + 33.33x + -62.9 = 0 Reorder the terms: -62.9 + 33.33x + 49.3x2 = 0 Solving -62.9 + 33.33x + 49.3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 49.3 the coefficient of the squared term: Divide each side by '49.3'. -1.275862069 + 0.6760649087x + x2 = 0 Move the constant term to the right: Add '1.275862069' to each side of the equation. -1.275862069 + 0.6760649087x + 1.275862069 + x2 = 0 + 1.275862069 Reorder the terms: -1.275862069 + 1.275862069 + 0.6760649087x + x2 = 0 + 1.275862069 Combine like terms: -1.275862069 + 1.275862069 = 0.000000000 0.000000000 + 0.6760649087x + x2 = 0 + 1.275862069 0.6760649087x + x2 = 0 + 1.275862069 Combine like terms: 0 + 1.275862069 = 1.275862069 0.6760649087x + x2 = 1.275862069 The x term is 0.6760649087x. Take half its coefficient (0.3380324544). Square it (0.1142659402) and add it to both sides. Add '0.1142659402' to each side of the equation. 0.6760649087x + 0.1142659402 + x2 = 1.275862069 + 0.1142659402 Reorder the terms: 0.1142659402 + 0.6760649087x + x2 = 1.275862069 + 0.1142659402 Combine like terms: 1.275862069 + 0.1142659402 = 1.3901280092 0.1142659402 + 0.6760649087x + x2 = 1.3901280092 Factor a perfect square on the left side: (x + 0.3380324544)(x + 0.3380324544) = 1.3901280092 Calculate the square root of the right side: 1.179036899 Break this problem into two subproblems by setting (x + 0.3380324544) equal to 1.179036899 and -1.179036899.Subproblem 1
x + 0.3380324544 = 1.179036899 Simplifying x + 0.3380324544 = 1.179036899 Reorder the terms: 0.3380324544 + x = 1.179036899 Solving 0.3380324544 + x = 1.179036899 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3380324544' to each side of the equation. 0.3380324544 + -0.3380324544 + x = 1.179036899 + -0.3380324544 Combine like terms: 0.3380324544 + -0.3380324544 = 0.0000000000 0.0000000000 + x = 1.179036899 + -0.3380324544 x = 1.179036899 + -0.3380324544 Combine like terms: 1.179036899 + -0.3380324544 = 0.8410044446 x = 0.8410044446 Simplifying x = 0.8410044446Subproblem 2
x + 0.3380324544 = -1.179036899 Simplifying x + 0.3380324544 = -1.179036899 Reorder the terms: 0.3380324544 + x = -1.179036899 Solving 0.3380324544 + x = -1.179036899 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3380324544' to each side of the equation. 0.3380324544 + -0.3380324544 + x = -1.179036899 + -0.3380324544 Combine like terms: 0.3380324544 + -0.3380324544 = 0.0000000000 0.0000000000 + x = -1.179036899 + -0.3380324544 x = -1.179036899 + -0.3380324544 Combine like terms: -1.179036899 + -0.3380324544 = -1.5170693534 x = -1.5170693534 Simplifying x = -1.5170693534Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.8410044446, -1.5170693534}
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