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Simplifying 3x(x + 4) = 7x + 4 Reorder the terms: 3x(4 + x) = 7x + 4 (4 * 3x + x * 3x) = 7x + 4 (12x + 3x2) = 7x + 4 Reorder the terms: 12x + 3x2 = 4 + 7x Solving 12x + 3x2 = 4 + 7x Solving for variable 'x'. Reorder the terms: -4 + 12x + -7x + 3x2 = 4 + 7x + -4 + -7x Combine like terms: 12x + -7x = 5x -4 + 5x + 3x2 = 4 + 7x + -4 + -7x Reorder the terms: -4 + 5x + 3x2 = 4 + -4 + 7x + -7x Combine like terms: 4 + -4 = 0 -4 + 5x + 3x2 = 0 + 7x + -7x -4 + 5x + 3x2 = 7x + -7x Combine like terms: 7x + -7x = 0 -4 + 5x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -1.333333333 + 1.666666667x + x2 = 0 Move the constant term to the right: Add '1.333333333' to each side of the equation. -1.333333333 + 1.666666667x + 1.333333333 + x2 = 0 + 1.333333333 Reorder the terms: -1.333333333 + 1.333333333 + 1.666666667x + x2 = 0 + 1.333333333 Combine like terms: -1.333333333 + 1.333333333 = 0.000000000 0.000000000 + 1.666666667x + x2 = 0 + 1.333333333 1.666666667x + x2 = 0 + 1.333333333 Combine like terms: 0 + 1.333333333 = 1.333333333 1.666666667x + x2 = 1.333333333 The x term is 1.666666667x. Take half its coefficient (0.8333333335). Square it (0.6944444447) and add it to both sides. Add '0.6944444447' to each side of the equation. 1.666666667x + 0.6944444447 + x2 = 1.333333333 + 0.6944444447 Reorder the terms: 0.6944444447 + 1.666666667x + x2 = 1.333333333 + 0.6944444447 Combine like terms: 1.333333333 + 0.6944444447 = 2.0277777777 0.6944444447 + 1.666666667x + x2 = 2.0277777777 Factor a perfect square on the left side: (x + 0.8333333335)(x + 0.8333333335) = 2.0277777777 Calculate the square root of the right side: 1.424000624 Break this problem into two subproblems by setting (x + 0.8333333335) equal to 1.424000624 and -1.424000624.Subproblem 1
x + 0.8333333335 = 1.424000624 Simplifying x + 0.8333333335 = 1.424000624 Reorder the terms: 0.8333333335 + x = 1.424000624 Solving 0.8333333335 + x = 1.424000624 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8333333335' to each side of the equation. 0.8333333335 + -0.8333333335 + x = 1.424000624 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + x = 1.424000624 + -0.8333333335 x = 1.424000624 + -0.8333333335 Combine like terms: 1.424000624 + -0.8333333335 = 0.5906672905 x = 0.5906672905 Simplifying x = 0.5906672905Subproblem 2
x + 0.8333333335 = -1.424000624 Simplifying x + 0.8333333335 = -1.424000624 Reorder the terms: 0.8333333335 + x = -1.424000624 Solving 0.8333333335 + x = -1.424000624 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8333333335' to each side of the equation. 0.8333333335 + -0.8333333335 + x = -1.424000624 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + x = -1.424000624 + -0.8333333335 x = -1.424000624 + -0.8333333335 Combine like terms: -1.424000624 + -0.8333333335 = -2.2573339575 x = -2.2573339575 Simplifying x = -2.2573339575Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.5906672905, -2.2573339575}
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