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Simplifying 3x + -1(-2x + 6) = 4x(x + -4) + 4 Reorder the terms: 3x + -1(6 + -2x) = 4x(x + -4) + 4 3x + (6 * -1 + -2x * -1) = 4x(x + -4) + 4 3x + (-6 + 2x) = 4x(x + -4) + 4 Reorder the terms: -6 + 3x + 2x = 4x(x + -4) + 4 Combine like terms: 3x + 2x = 5x -6 + 5x = 4x(x + -4) + 4 Reorder the terms: -6 + 5x = 4x(-4 + x) + 4 -6 + 5x = (-4 * 4x + x * 4x) + 4 -6 + 5x = (-16x + 4x2) + 4 Reorder the terms: -6 + 5x = 4 + -16x + 4x2 Solving -6 + 5x = 4 + -16x + 4x2 Solving for variable 'x'. Reorder the terms: -6 + -4 + 5x + 16x + -4x2 = 4 + -16x + 4x2 + -4 + 16x + -4x2 Combine like terms: -6 + -4 = -10 -10 + 5x + 16x + -4x2 = 4 + -16x + 4x2 + -4 + 16x + -4x2 Combine like terms: 5x + 16x = 21x -10 + 21x + -4x2 = 4 + -16x + 4x2 + -4 + 16x + -4x2 Reorder the terms: -10 + 21x + -4x2 = 4 + -4 + -16x + 16x + 4x2 + -4x2 Combine like terms: 4 + -4 = 0 -10 + 21x + -4x2 = 0 + -16x + 16x + 4x2 + -4x2 -10 + 21x + -4x2 = -16x + 16x + 4x2 + -4x2 Combine like terms: -16x + 16x = 0 -10 + 21x + -4x2 = 0 + 4x2 + -4x2 -10 + 21x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 -10 + 21x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. 2.5 + -5.25x + x2 = 0 Move the constant term to the right: Add '-2.5' to each side of the equation. 2.5 + -5.25x + -2.5 + x2 = 0 + -2.5 Reorder the terms: 2.5 + -2.5 + -5.25x + x2 = 0 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + -5.25x + x2 = 0 + -2.5 -5.25x + x2 = 0 + -2.5 Combine like terms: 0 + -2.5 = -2.5 -5.25x + x2 = -2.5 The x term is -5.25x. Take half its coefficient (-2.625). Square it (6.890625) and add it to both sides. Add '6.890625' to each side of the equation. -5.25x + 6.890625 + x2 = -2.5 + 6.890625 Reorder the terms: 6.890625 + -5.25x + x2 = -2.5 + 6.890625 Combine like terms: -2.5 + 6.890625 = 4.390625 6.890625 + -5.25x + x2 = 4.390625 Factor a perfect square on the left side: (x + -2.625)(x + -2.625) = 4.390625 Calculate the square root of the right side: 2.095381827 Break this problem into two subproblems by setting (x + -2.625) equal to 2.095381827 and -2.095381827.Subproblem 1
x + -2.625 = 2.095381827 Simplifying x + -2.625 = 2.095381827 Reorder the terms: -2.625 + x = 2.095381827 Solving -2.625 + x = 2.095381827 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.625' to each side of the equation. -2.625 + 2.625 + x = 2.095381827 + 2.625 Combine like terms: -2.625 + 2.625 = 0.000 0.000 + x = 2.095381827 + 2.625 x = 2.095381827 + 2.625 Combine like terms: 2.095381827 + 2.625 = 4.720381827 x = 4.720381827 Simplifying x = 4.720381827Subproblem 2
x + -2.625 = -2.095381827 Simplifying x + -2.625 = -2.095381827 Reorder the terms: -2.625 + x = -2.095381827 Solving -2.625 + x = -2.095381827 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.625' to each side of the equation. -2.625 + 2.625 + x = -2.095381827 + 2.625 Combine like terms: -2.625 + 2.625 = 0.000 0.000 + x = -2.095381827 + 2.625 x = -2.095381827 + 2.625 Combine like terms: -2.095381827 + 2.625 = 0.529618173 x = 0.529618173 Simplifying x = 0.529618173Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.720381827, 0.529618173}
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