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Simplifying 3x2 + 32x + 26 = -4 Reorder the terms: 26 + 32x + 3x2 = -4 Solving 26 + 32x + 3x2 = -4 Solving for variable 'x'. Reorder the terms: 26 + 4 + 32x + 3x2 = -4 + 4 Combine like terms: 26 + 4 = 30 30 + 32x + 3x2 = -4 + 4 Combine like terms: -4 + 4 = 0 30 + 32x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 10 + 10.66666667x + x2 = 0 Move the constant term to the right: Add '-10' to each side of the equation. 10 + 10.66666667x + -10 + x2 = 0 + -10 Reorder the terms: 10 + -10 + 10.66666667x + x2 = 0 + -10 Combine like terms: 10 + -10 = 0 0 + 10.66666667x + x2 = 0 + -10 10.66666667x + x2 = 0 + -10 Combine like terms: 0 + -10 = -10 10.66666667x + x2 = -10 The x term is 10.66666667x. Take half its coefficient (5.333333335). Square it (28.44444446) and add it to both sides. Add '28.44444446' to each side of the equation. 10.66666667x + 28.44444446 + x2 = -10 + 28.44444446 Reorder the terms: 28.44444446 + 10.66666667x + x2 = -10 + 28.44444446 Combine like terms: -10 + 28.44444446 = 18.44444446 28.44444446 + 10.66666667x + x2 = 18.44444446 Factor a perfect square on the left side: (x + 5.333333335)(x + 5.333333335) = 18.44444446 Calculate the square root of the right side: 4.294699577 Break this problem into two subproblems by setting (x + 5.333333335) equal to 4.294699577 and -4.294699577.Subproblem 1
x + 5.333333335 = 4.294699577 Simplifying x + 5.333333335 = 4.294699577 Reorder the terms: 5.333333335 + x = 4.294699577 Solving 5.333333335 + x = 4.294699577 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.333333335' to each side of the equation. 5.333333335 + -5.333333335 + x = 4.294699577 + -5.333333335 Combine like terms: 5.333333335 + -5.333333335 = 0.000000000 0.000000000 + x = 4.294699577 + -5.333333335 x = 4.294699577 + -5.333333335 Combine like terms: 4.294699577 + -5.333333335 = -1.038633758 x = -1.038633758 Simplifying x = -1.038633758Subproblem 2
x + 5.333333335 = -4.294699577 Simplifying x + 5.333333335 = -4.294699577 Reorder the terms: 5.333333335 + x = -4.294699577 Solving 5.333333335 + x = -4.294699577 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.333333335' to each side of the equation. 5.333333335 + -5.333333335 + x = -4.294699577 + -5.333333335 Combine like terms: 5.333333335 + -5.333333335 = 0.000000000 0.000000000 + x = -4.294699577 + -5.333333335 x = -4.294699577 + -5.333333335 Combine like terms: -4.294699577 + -5.333333335 = -9.628032912 x = -9.628032912 Simplifying x = -9.628032912Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.038633758, -9.628032912}
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