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Simplifying 6X = 63 + -2X2 Solving 6X = 63 + -2X2 Solving for variable 'X'. Reorder the terms: -63 + 6X + 2X2 = 63 + -2X2 + -63 + 2X2 Reorder the terms: -63 + 6X + 2X2 = 63 + -63 + -2X2 + 2X2 Combine like terms: 63 + -63 = 0 -63 + 6X + 2X2 = 0 + -2X2 + 2X2 -63 + 6X + 2X2 = -2X2 + 2X2 Combine like terms: -2X2 + 2X2 = 0 -63 + 6X + 2X2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -31.5 + 3X + X2 = 0 Move the constant term to the right: Add '31.5' to each side of the equation. -31.5 + 3X + 31.5 + X2 = 0 + 31.5 Reorder the terms: -31.5 + 31.5 + 3X + X2 = 0 + 31.5 Combine like terms: -31.5 + 31.5 = 0.0 0.0 + 3X + X2 = 0 + 31.5 3X + X2 = 0 + 31.5 Combine like terms: 0 + 31.5 = 31.5 3X + X2 = 31.5 The X term is 3X. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3X + 2.25 + X2 = 31.5 + 2.25 Reorder the terms: 2.25 + 3X + X2 = 31.5 + 2.25 Combine like terms: 31.5 + 2.25 = 33.75 2.25 + 3X + X2 = 33.75 Factor a perfect square on the left side: (X + 1.5)(X + 1.5) = 33.75 Calculate the square root of the right side: 5.809475019 Break this problem into two subproblems by setting (X + 1.5) equal to 5.809475019 and -5.809475019.Subproblem 1
X + 1.5 = 5.809475019 Simplifying X + 1.5 = 5.809475019 Reorder the terms: 1.5 + X = 5.809475019 Solving 1.5 + X = 5.809475019 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + X = 5.809475019 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + X = 5.809475019 + -1.5 X = 5.809475019 + -1.5 Combine like terms: 5.809475019 + -1.5 = 4.309475019 X = 4.309475019 Simplifying X = 4.309475019Subproblem 2
X + 1.5 = -5.809475019 Simplifying X + 1.5 = -5.809475019 Reorder the terms: 1.5 + X = -5.809475019 Solving 1.5 + X = -5.809475019 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + X = -5.809475019 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + X = -5.809475019 + -1.5 X = -5.809475019 + -1.5 Combine like terms: -5.809475019 + -1.5 = -7.309475019 X = -7.309475019 Simplifying X = -7.309475019Solution
The solution to the problem is based on the solutions from the subproblems. X = {4.309475019, -7.309475019}
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