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Simplifying 4x2 + -15x + 19 = 3x + 4 Reorder the terms: 19 + -15x + 4x2 = 3x + 4 Reorder the terms: 19 + -15x + 4x2 = 4 + 3x Solving 19 + -15x + 4x2 = 4 + 3x Solving for variable 'x'. Reorder the terms: 19 + -4 + -15x + -3x + 4x2 = 4 + 3x + -4 + -3x Combine like terms: 19 + -4 = 15 15 + -15x + -3x + 4x2 = 4 + 3x + -4 + -3x Combine like terms: -15x + -3x = -18x 15 + -18x + 4x2 = 4 + 3x + -4 + -3x Reorder the terms: 15 + -18x + 4x2 = 4 + -4 + 3x + -3x Combine like terms: 4 + -4 = 0 15 + -18x + 4x2 = 0 + 3x + -3x 15 + -18x + 4x2 = 3x + -3x Combine like terms: 3x + -3x = 0 15 + -18x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 3.75 + -4.5x + x2 = 0 Move the constant term to the right: Add '-3.75' to each side of the equation. 3.75 + -4.5x + -3.75 + x2 = 0 + -3.75 Reorder the terms: 3.75 + -3.75 + -4.5x + x2 = 0 + -3.75 Combine like terms: 3.75 + -3.75 = 0.00 0.00 + -4.5x + x2 = 0 + -3.75 -4.5x + x2 = 0 + -3.75 Combine like terms: 0 + -3.75 = -3.75 -4.5x + x2 = -3.75 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 = -3.75 + 5.0625 Reorder the terms: 5.0625 + -4.5x + x2 = -3.75 + 5.0625 Combine like terms: -3.75 + 5.0625 = 1.3125 5.0625 + -4.5x + x2 = 1.3125 Factor a perfect square on the left side: (x + -2.25)(x + -2.25) = 1.3125 Calculate the square root of the right side: 1.145643924 Break this problem into two subproblems by setting (x + -2.25) equal to 1.145643924 and -1.145643924.Subproblem 1
x + -2.25 = 1.145643924 Simplifying x + -2.25 = 1.145643924 Reorder the terms: -2.25 + x = 1.145643924 Solving -2.25 + x = 1.145643924 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 = 1.145643924 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + x = 1.145643924 + 2.25 x = 1.145643924 + 2.25 Combine like terms: 1.145643924 + 2.25 = 3.395643924 x = 3.395643924 Simplifying x = 3.395643924Subproblem 2
x + -2.25 = -1.145643924 Simplifying x + -2.25 = -1.145643924 Reorder the terms: -2.25 + x = -1.145643924 Solving -2.25 + x = -1.145643924 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 = -1.145643924 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + x = -1.145643924 + 2.25 x = -1.145643924 + 2.25 Combine like terms: -1.145643924 + 2.25 = 1.104356076 x = 1.104356076 Simplifying x = 1.104356076Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.395643924, 1.104356076}
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