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Simplifying 7x(x + 3) + 4 = 3x(x + 4) Reorder the terms: 7x(3 + x) + 4 = 3x(x + 4) (3 * 7x + x * 7x) + 4 = 3x(x + 4) (21x + 7x2) + 4 = 3x(x + 4) Reorder the terms: 4 + 21x + 7x2 = 3x(x + 4) Reorder the terms: 4 + 21x + 7x2 = 3x(4 + x) 4 + 21x + 7x2 = (4 * 3x + x * 3x) 4 + 21x + 7x2 = (12x + 3x2) Solving 4 + 21x + 7x2 = 12x + 3x2 Solving for variable 'x'. Reorder the terms: 4 + 21x + -12x + 7x2 + -3x2 = 12x + 3x2 + -12x + -3x2 Combine like terms: 21x + -12x = 9x 4 + 9x + 7x2 + -3x2 = 12x + 3x2 + -12x + -3x2 Combine like terms: 7x2 + -3x2 = 4x2 4 + 9x + 4x2 = 12x + 3x2 + -12x + -3x2 Reorder the terms: 4 + 9x + 4x2 = 12x + -12x + 3x2 + -3x2 Combine like terms: 12x + -12x = 0 4 + 9x + 4x2 = 0 + 3x2 + -3x2 4 + 9x + 4x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 4 + 9x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 1 + 2.25x + x2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + 2.25x + -1 + x2 = 0 + -1 Reorder the terms: 1 + -1 + 2.25x + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2.25x + x2 = 0 + -1 2.25x + x2 = 0 + -1 Combine like terms: 0 + -1 = -1 2.25x + x2 = -1 The x term is 2.25x. Take half its coefficient (1.125). Square it (1.265625) and add it to both sides. Add '1.265625' to each side of the equation. 2.25x + 1.265625 + x2 = -1 + 1.265625 Reorder the terms: 1.265625 + 2.25x + x2 = -1 + 1.265625 Combine like terms: -1 + 1.265625 = 0.265625 1.265625 + 2.25x + x2 = 0.265625 Factor a perfect square on the left side: (x + 1.125)(x + 1.125) = 0.265625 Calculate the square root of the right side: 0.515388203 Break this problem into two subproblems by setting (x + 1.125) equal to 0.515388203 and -0.515388203.Subproblem 1
x + 1.125 = 0.515388203 Simplifying x + 1.125 = 0.515388203 Reorder the terms: 1.125 + x = 0.515388203 Solving 1.125 + x = 0.515388203 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.125' to each side of the equation. 1.125 + -1.125 + x = 0.515388203 + -1.125 Combine like terms: 1.125 + -1.125 = 0.000 0.000 + x = 0.515388203 + -1.125 x = 0.515388203 + -1.125 Combine like terms: 0.515388203 + -1.125 = -0.609611797 x = -0.609611797 Simplifying x = -0.609611797Subproblem 2
x + 1.125 = -0.515388203 Simplifying x + 1.125 = -0.515388203 Reorder the terms: 1.125 + x = -0.515388203 Solving 1.125 + x = -0.515388203 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.125' to each side of the equation. 1.125 + -1.125 + x = -0.515388203 + -1.125 Combine like terms: 1.125 + -1.125 = 0.000 0.000 + x = -0.515388203 + -1.125 x = -0.515388203 + -1.125 Combine like terms: -0.515388203 + -1.125 = -1.640388203 x = -1.640388203 Simplifying x = -1.640388203Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.609611797, -1.640388203}
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