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Simplifying 4x2 + -16x + 12 = (2x + -1) Reorder the terms: 12 + -16x + 4x2 = (2x + -1) Reorder the terms: 12 + -16x + 4x2 = (-1 + 2x) Remove parenthesis around (-1 + 2x) 12 + -16x + 4x2 = -1 + 2x Solving 12 + -16x + 4x2 = -1 + 2x Solving for variable 'x'. Reorder the terms: 12 + 1 + -16x + -2x + 4x2 = -1 + 2x + 1 + -2x Combine like terms: 12 + 1 = 13 13 + -16x + -2x + 4x2 = -1 + 2x + 1 + -2x Combine like terms: -16x + -2x = -18x 13 + -18x + 4x2 = -1 + 2x + 1 + -2x Reorder the terms: 13 + -18x + 4x2 = -1 + 1 + 2x + -2x Combine like terms: -1 + 1 = 0 13 + -18x + 4x2 = 0 + 2x + -2x 13 + -18x + 4x2 = 2x + -2x Combine like terms: 2x + -2x = 0 13 + -18x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 3.25 + -4.5x + x2 = 0 Move the constant term to the right: Add '-3.25' to each side of the equation. 3.25 + -4.5x + -3.25 + x2 = 0 + -3.25 Reorder the terms: 3.25 + -3.25 + -4.5x + x2 = 0 + -3.25 Combine like terms: 3.25 + -3.25 = 0.00 0.00 + -4.5x + x2 = 0 + -3.25 -4.5x + x2 = 0 + -3.25 Combine like terms: 0 + -3.25 = -3.25 -4.5x + x2 = -3.25 The x term is -4.5x. Take half its coefficient (-2.25). Square it (5.0625) and add it to both sides. Add '5.0625' to each side of the equation. -4.5x + 5.0625 + x2 = -3.25 + 5.0625 Reorder the terms: 5.0625 + -4.5x + x2 = -3.25 + 5.0625 Combine like terms: -3.25 + 5.0625 = 1.8125 5.0625 + -4.5x + x2 = 1.8125 Factor a perfect square on the left side: (x + -2.25)(x + -2.25) = 1.8125 Calculate the square root of the right side: 1.346291202 Break this problem into two subproblems by setting (x + -2.25) equal to 1.346291202 and -1.346291202.Subproblem 1
x + -2.25 = 1.346291202 Simplifying x + -2.25 = 1.346291202 Reorder the terms: -2.25 + x = 1.346291202 Solving -2.25 + x = 1.346291202 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + x = 1.346291202 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + x = 1.346291202 + 2.25 x = 1.346291202 + 2.25 Combine like terms: 1.346291202 + 2.25 = 3.596291202 x = 3.596291202 Simplifying x = 3.596291202Subproblem 2
x + -2.25 = -1.346291202 Simplifying x + -2.25 = -1.346291202 Reorder the terms: -2.25 + x = -1.346291202 Solving -2.25 + x = -1.346291202 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + x = -1.346291202 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + x = -1.346291202 + 2.25 x = -1.346291202 + 2.25 Combine like terms: -1.346291202 + 2.25 = 0.903708798 x = 0.903708798 Simplifying x = 0.903708798Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.596291202, 0.903708798}
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