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Simplifying 234x2 + (-3455) + (3445x + (-3345)) = 236 234x2 + -3455 + (3445x + (-3345)) = 236 234x2 + -3455 + (3445x + -3345) = 236 Reorder the terms: 234x2 + -3455 + (-3345 + 3445x) = 236 Remove parenthesis around (-3345 + 3445x) 234x2 + -3455 + -3345 + 3445x = 236 Reorder the terms: -3455 + -3345 + 3445x + 234x2 = 236 Combine like terms: -3455 + -3345 = -6800 -6800 + 3445x + 234x2 = 236 Solving -6800 + 3445x + 234x2 = 236 Solving for variable 'x'. Reorder the terms: -6800 + -236 + 3445x + 234x2 = 236 + -236 Combine like terms: -6800 + -236 = -7036 -7036 + 3445x + 234x2 = 236 + -236 Combine like terms: 236 + -236 = 0 -7036 + 3445x + 234x2 = 0 Begin completing the square. Divide all terms by 234 the coefficient of the squared term: Divide each side by '234'. -30.06837607 + 14.72222222x + x2 = 0 Move the constant term to the right: Add '30.06837607' to each side of the equation. -30.06837607 + 14.72222222x + 30.06837607 + x2 = 0 + 30.06837607 Reorder the terms: -30.06837607 + 30.06837607 + 14.72222222x + x2 = 0 + 30.06837607 Combine like terms: -30.06837607 + 30.06837607 = 0.00000000 0.00000000 + 14.72222222x + x2 = 0 + 30.06837607 14.72222222x + x2 = 0 + 30.06837607 Combine like terms: 0 + 30.06837607 = 30.06837607 14.72222222x + x2 = 30.06837607 The x term is 14.72222222x. Take half its coefficient (7.36111111). Square it (54.18595677) and add it to both sides. Add '54.18595677' to each side of the equation. 14.72222222x + 54.18595677 + x2 = 30.06837607 + 54.18595677 Reorder the terms: 54.18595677 + 14.72222222x + x2 = 30.06837607 + 54.18595677 Combine like terms: 30.06837607 + 54.18595677 = 84.25433284 54.18595677 + 14.72222222x + x2 = 84.25433284 Factor a perfect square on the left side: (x + 7.36111111)(x + 7.36111111) = 84.25433284 Calculate the square root of the right side: 9.179015897 Break this problem into two subproblems by setting (x + 7.36111111) equal to 9.179015897 and -9.179015897.Subproblem 1
x + 7.36111111 = 9.179015897 Simplifying x + 7.36111111 = 9.179015897 Reorder the terms: 7.36111111 + x = 9.179015897 Solving 7.36111111 + x = 9.179015897 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.36111111' to each side of the equation. 7.36111111 + -7.36111111 + x = 9.179015897 + -7.36111111 Combine like terms: 7.36111111 + -7.36111111 = 0.00000000 0.00000000 + x = 9.179015897 + -7.36111111 x = 9.179015897 + -7.36111111 Combine like terms: 9.179015897 + -7.36111111 = 1.817904787 x = 1.817904787 Simplifying x = 1.817904787Subproblem 2
x + 7.36111111 = -9.179015897 Simplifying x + 7.36111111 = -9.179015897 Reorder the terms: 7.36111111 + x = -9.179015897 Solving 7.36111111 + x = -9.179015897 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.36111111' to each side of the equation. 7.36111111 + -7.36111111 + x = -9.179015897 + -7.36111111 Combine like terms: 7.36111111 + -7.36111111 = 0.00000000 0.00000000 + x = -9.179015897 + -7.36111111 x = -9.179015897 + -7.36111111 Combine like terms: -9.179015897 + -7.36111111 = -16.540127007 x = -16.540127007 Simplifying x = -16.540127007Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.817904787, -16.540127007}
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