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Simplifying 4X2 + -29X = 7 + 0 Reorder the terms: -29X + 4X2 = 7 + 0 Combine like terms: 7 + 0 = 7 -29X + 4X2 = 7 Solving -29X + 4X2 = 7 Solving for variable 'X'. Reorder the terms: -7 + -29X + 4X2 = 7 + -7 Combine like terms: 7 + -7 = 0 -7 + -29X + 4X2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -1.75 + -7.25X + X2 = 0 Move the constant term to the right: Add '1.75' to each side of the equation. -1.75 + -7.25X + 1.75 + X2 = 0 + 1.75 Reorder the terms: -1.75 + 1.75 + -7.25X + X2 = 0 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + -7.25X + X2 = 0 + 1.75 -7.25X + X2 = 0 + 1.75 Combine like terms: 0 + 1.75 = 1.75 -7.25X + X2 = 1.75 The X term is -7.25X. Take half its coefficient (-3.625). Square it (13.140625) and add it to both sides. Add '13.140625' to each side of the equation. -7.25X + 13.140625 + X2 = 1.75 + 13.140625 Reorder the terms: 13.140625 + -7.25X + X2 = 1.75 + 13.140625 Combine like terms: 1.75 + 13.140625 = 14.890625 13.140625 + -7.25X + X2 = 14.890625 Factor a perfect square on the left side: (X + -3.625)(X + -3.625) = 14.890625 Calculate the square root of the right side: 3.85883726 Break this problem into two subproblems by setting (X + -3.625) equal to 3.85883726 and -3.85883726.Subproblem 1
X + -3.625 = 3.85883726 Simplifying X + -3.625 = 3.85883726 Reorder the terms: -3.625 + X = 3.85883726 Solving -3.625 + X = 3.85883726 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '3.625' to each side of the equation. -3.625 + 3.625 + X = 3.85883726 + 3.625 Combine like terms: -3.625 + 3.625 = 0.000 0.000 + X = 3.85883726 + 3.625 X = 3.85883726 + 3.625 Combine like terms: 3.85883726 + 3.625 = 7.48383726 X = 7.48383726 Simplifying X = 7.48383726Subproblem 2
X + -3.625 = -3.85883726 Simplifying X + -3.625 = -3.85883726 Reorder the terms: -3.625 + X = -3.85883726 Solving -3.625 + X = -3.85883726 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '3.625' to each side of the equation. -3.625 + 3.625 + X = -3.85883726 + 3.625 Combine like terms: -3.625 + 3.625 = 0.000 0.000 + X = -3.85883726 + 3.625 X = -3.85883726 + 3.625 Combine like terms: -3.85883726 + 3.625 = -0.23383726 X = -0.23383726 Simplifying X = -0.23383726Solution
The solution to the problem is based on the solutions from the subproblems. X = {7.48383726, -0.23383726}
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