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Simplifying 4x2 + -15x + 12 = 4x + 5 Reorder the terms: 12 + -15x + 4x2 = 4x + 5 Reorder the terms: 12 + -15x + 4x2 = 5 + 4x Solving 12 + -15x + 4x2 = 5 + 4x Solving for variable 'x'. Reorder the terms: 12 + -5 + -15x + -4x + 4x2 = 5 + 4x + -5 + -4x Combine like terms: 12 + -5 = 7 7 + -15x + -4x + 4x2 = 5 + 4x + -5 + -4x Combine like terms: -15x + -4x = -19x 7 + -19x + 4x2 = 5 + 4x + -5 + -4x Reorder the terms: 7 + -19x + 4x2 = 5 + -5 + 4x + -4x Combine like terms: 5 + -5 = 0 7 + -19x + 4x2 = 0 + 4x + -4x 7 + -19x + 4x2 = 4x + -4x Combine like terms: 4x + -4x = 0 7 + -19x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 1.75 + -4.75x + x2 = 0 Move the constant term to the right: Add '-1.75' to each side of the equation. 1.75 + -4.75x + -1.75 + x2 = 0 + -1.75 Reorder the terms: 1.75 + -1.75 + -4.75x + x2 = 0 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + -4.75x + x2 = 0 + -1.75 -4.75x + x2 = 0 + -1.75 Combine like terms: 0 + -1.75 = -1.75 -4.75x + x2 = -1.75 The x term is -4.75x. Take half its coefficient (-2.375). Square it (5.640625) and add it to both sides. Add '5.640625' to each side of the equation. -4.75x + 5.640625 + x2 = -1.75 + 5.640625 Reorder the terms: 5.640625 + -4.75x + x2 = -1.75 + 5.640625 Combine like terms: -1.75 + 5.640625 = 3.890625 5.640625 + -4.75x + x2 = 3.890625 Factor a perfect square on the left side: (x + -2.375)(x + -2.375) = 3.890625 Calculate the square root of the right side: 1.97246673 Break this problem into two subproblems by setting (x + -2.375) equal to 1.97246673 and -1.97246673.Subproblem 1
x + -2.375 = 1.97246673 Simplifying x + -2.375 = 1.97246673 Reorder the terms: -2.375 + x = 1.97246673 Solving -2.375 + x = 1.97246673 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.375' to each side of the equation. -2.375 + 2.375 + x = 1.97246673 + 2.375 Combine like terms: -2.375 + 2.375 = 0.000 0.000 + x = 1.97246673 + 2.375 x = 1.97246673 + 2.375 Combine like terms: 1.97246673 + 2.375 = 4.34746673 x = 4.34746673 Simplifying x = 4.34746673Subproblem 2
x + -2.375 = -1.97246673 Simplifying x + -2.375 = -1.97246673 Reorder the terms: -2.375 + x = -1.97246673 Solving -2.375 + x = -1.97246673 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.375' to each side of the equation. -2.375 + 2.375 + x = -1.97246673 + 2.375 Combine like terms: -2.375 + 2.375 = 0.000 0.000 + x = -1.97246673 + 2.375 x = -1.97246673 + 2.375 Combine like terms: -1.97246673 + 2.375 = 0.40253327 x = 0.40253327 Simplifying x = 0.40253327Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.34746673, 0.40253327}
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