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Simplifying 4(2.1x + 6) = 1.4x(4.5x + -0.24) Reorder the terms: 4(6 + 2.1x) = 1.4x(4.5x + -0.24) (6 * 4 + 2.1x * 4) = 1.4x(4.5x + -0.24) (24 + 8.4x) = 1.4x(4.5x + -0.24) Reorder the terms: 24 + 8.4x = 1.4x(-0.24 + 4.5x) 24 + 8.4x = (-0.24 * 1.4x + 4.5x * 1.4x) 24 + 8.4x = (-0.336x + 6.3x2) Solving 24 + 8.4x = -0.336x + 6.3x2 Solving for variable 'x'. Combine like terms: 8.4x + 0.336x = 8.736x 24 + 8.736x + -6.3x2 = -0.336x + 6.3x2 + 0.336x + -6.3x2 Reorder the terms: 24 + 8.736x + -6.3x2 = -0.336x + 0.336x + 6.3x2 + -6.3x2 Combine like terms: -0.336x + 0.336x = 0.000 24 + 8.736x + -6.3x2 = 0.000 + 6.3x2 + -6.3x2 24 + 8.736x + -6.3x2 = 6.3x2 + -6.3x2 Combine like terms: 6.3x2 + -6.3x2 = 0.0 24 + 8.736x + -6.3x2 = 0.0 Begin completing the square. Divide all terms by -6.3 the coefficient of the squared term: Divide each side by '-6.3'. -3.80952381 + -1.386666667x + x2 = 0 Move the constant term to the right: Add '3.80952381' to each side of the equation. -3.80952381 + -1.386666667x + 3.80952381 + x2 = 0 + 3.80952381 Reorder the terms: -3.80952381 + 3.80952381 + -1.386666667x + x2 = 0 + 3.80952381 Combine like terms: -3.80952381 + 3.80952381 = 0.00000000 0.00000000 + -1.386666667x + x2 = 0 + 3.80952381 -1.386666667x + x2 = 0 + 3.80952381 Combine like terms: 0 + 3.80952381 = 3.80952381 -1.386666667x + x2 = 3.80952381 The x term is -1.386666667x. Take half its coefficient (-0.6933333335). Square it (0.4807111113) and add it to both sides. Add '0.4807111113' to each side of the equation. -1.386666667x + 0.4807111113 + x2 = 3.80952381 + 0.4807111113 Reorder the terms: 0.4807111113 + -1.386666667x + x2 = 3.80952381 + 0.4807111113 Combine like terms: 3.80952381 + 0.4807111113 = 4.2902349213 0.4807111113 + -1.386666667x + x2 = 4.2902349213 Factor a perfect square on the left side: (x + -0.6933333335)(x + -0.6933333335) = 4.2902349213 Calculate the square root of the right side: 2.071288227 Break this problem into two subproblems by setting (x + -0.6933333335) equal to 2.071288227 and -2.071288227.Subproblem 1
x + -0.6933333335 = 2.071288227 Simplifying x + -0.6933333335 = 2.071288227 Reorder the terms: -0.6933333335 + x = 2.071288227 Solving -0.6933333335 + x = 2.071288227 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6933333335' to each side of the equation. -0.6933333335 + 0.6933333335 + x = 2.071288227 + 0.6933333335 Combine like terms: -0.6933333335 + 0.6933333335 = 0.0000000000 0.0000000000 + x = 2.071288227 + 0.6933333335 x = 2.071288227 + 0.6933333335 Combine like terms: 2.071288227 + 0.6933333335 = 2.7646215605 x = 2.7646215605 Simplifying x = 2.7646215605Subproblem 2
x + -0.6933333335 = -2.071288227 Simplifying x + -0.6933333335 = -2.071288227 Reorder the terms: -0.6933333335 + x = -2.071288227 Solving -0.6933333335 + x = -2.071288227 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6933333335' to each side of the equation. -0.6933333335 + 0.6933333335 + x = -2.071288227 + 0.6933333335 Combine like terms: -0.6933333335 + 0.6933333335 = 0.0000000000 0.0000000000 + x = -2.071288227 + 0.6933333335 x = -2.071288227 + 0.6933333335 Combine like terms: -2.071288227 + 0.6933333335 = -1.3779548935 x = -1.3779548935 Simplifying x = -1.3779548935Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.7646215605, -1.3779548935}
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