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Simplifying 33 = x + 8(x2 + -6x + -7) Reorder the terms: 33 = x + 8(-7 + -6x + x2) 33 = x + (-7 * 8 + -6x * 8 + x2 * 8) 33 = x + (-56 + -48x + 8x2) Reorder the terms: 33 = -56 + x + -48x + 8x2 Combine like terms: x + -48x = -47x 33 = -56 + -47x + 8x2 Solving 33 = -56 + -47x + 8x2 Solving for variable 'x'. Combine like terms: 33 + 56 = 89 89 + 47x + -8x2 = -56 + -47x + 8x2 + 56 + 47x + -8x2 Reorder the terms: 89 + 47x + -8x2 = -56 + 56 + -47x + 47x + 8x2 + -8x2 Combine like terms: -56 + 56 = 0 89 + 47x + -8x2 = 0 + -47x + 47x + 8x2 + -8x2 89 + 47x + -8x2 = -47x + 47x + 8x2 + -8x2 Combine like terms: -47x + 47x = 0 89 + 47x + -8x2 = 0 + 8x2 + -8x2 89 + 47x + -8x2 = 8x2 + -8x2 Combine like terms: 8x2 + -8x2 = 0 89 + 47x + -8x2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -11.125 + -5.875x + x2 = 0 Move the constant term to the right: Add '11.125' to each side of the equation. -11.125 + -5.875x + 11.125 + x2 = 0 + 11.125 Reorder the terms: -11.125 + 11.125 + -5.875x + x2 = 0 + 11.125 Combine like terms: -11.125 + 11.125 = 0.000 0.000 + -5.875x + x2 = 0 + 11.125 -5.875x + x2 = 0 + 11.125 Combine like terms: 0 + 11.125 = 11.125 -5.875x + x2 = 11.125 The x term is -5.875x. Take half its coefficient (-2.9375). Square it (8.62890625) and add it to both sides. Add '8.62890625' to each side of the equation. -5.875x + 8.62890625 + x2 = 11.125 + 8.62890625 Reorder the terms: 8.62890625 + -5.875x + x2 = 11.125 + 8.62890625 Combine like terms: 11.125 + 8.62890625 = 19.75390625 8.62890625 + -5.875x + x2 = 19.75390625 Factor a perfect square on the left side: (x + -2.9375)(x + -2.9375) = 19.75390625 Calculate the square root of the right side: 4.444536674 Break this problem into two subproblems by setting (x + -2.9375) equal to 4.444536674 and -4.444536674.Subproblem 1
x + -2.9375 = 4.444536674 Simplifying x + -2.9375 = 4.444536674 Reorder the terms: -2.9375 + x = 4.444536674 Solving -2.9375 + x = 4.444536674 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.9375' to each side of the equation. -2.9375 + 2.9375 + x = 4.444536674 + 2.9375 Combine like terms: -2.9375 + 2.9375 = 0.0000 0.0000 + x = 4.444536674 + 2.9375 x = 4.444536674 + 2.9375 Combine like terms: 4.444536674 + 2.9375 = 7.382036674 x = 7.382036674 Simplifying x = 7.382036674Subproblem 2
x + -2.9375 = -4.444536674 Simplifying x + -2.9375 = -4.444536674 Reorder the terms: -2.9375 + x = -4.444536674 Solving -2.9375 + x = -4.444536674 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.9375' to each side of the equation. -2.9375 + 2.9375 + x = -4.444536674 + 2.9375 Combine like terms: -2.9375 + 2.9375 = 0.0000 0.0000 + x = -4.444536674 + 2.9375 x = -4.444536674 + 2.9375 Combine like terms: -4.444536674 + 2.9375 = -1.507036674 x = -1.507036674 Simplifying x = -1.507036674Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.382036674, -1.507036674}
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