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Simplifying 4x2 + -12x + -63 = 0 Reorder the terms: -63 + -12x + 4x2 = 0 Solving -63 + -12x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -15.75 + -3x + x2 = 0 Move the constant term to the right: Add '15.75' to each side of the equation. -15.75 + -3x + 15.75 + x2 = 0 + 15.75 Reorder the terms: -15.75 + 15.75 + -3x + x2 = 0 + 15.75 Combine like terms: -15.75 + 15.75 = 0.00 0.00 + -3x + x2 = 0 + 15.75 -3x + x2 = 0 + 15.75 Combine like terms: 0 + 15.75 = 15.75 -3x + x2 = 15.75 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 = 15.75 + 2.25 Reorder the terms: 2.25 + -3x + x2 = 15.75 + 2.25 Combine like terms: 15.75 + 2.25 = 18 2.25 + -3x + x2 = 18 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 18 Calculate the square root of the right side: 4.242640687 Break this problem into two subproblems by setting (x + -1.5) equal to 4.242640687 and -4.242640687.Subproblem 1
x + -1.5 = 4.242640687 Simplifying x + -1.5 = 4.242640687 Reorder the terms: -1.5 + x = 4.242640687 Solving -1.5 + x = 4.242640687 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 = 4.242640687 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 4.242640687 + 1.5 x = 4.242640687 + 1.5 Combine like terms: 4.242640687 + 1.5 = 5.742640687 x = 5.742640687 Simplifying x = 5.742640687Subproblem 2
x + -1.5 = -4.242640687 Simplifying x + -1.5 = -4.242640687 Reorder the terms: -1.5 + x = -4.242640687 Solving -1.5 + x = -4.242640687 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 = -4.242640687 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -4.242640687 + 1.5 x = -4.242640687 + 1.5 Combine like terms: -4.242640687 + 1.5 = -2.742640687 x = -2.742640687 Simplifying x = -2.742640687Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.742640687, -2.742640687}
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