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Simplifying 4x2 + 14x + 21 = 3x2 + -6 Reorder the terms: 21 + 14x + 4x2 = 3x2 + -6 Reorder the terms: 21 + 14x + 4x2 = -6 + 3x2 Solving 21 + 14x + 4x2 = -6 + 3x2 Solving for variable 'x'. Reorder the terms: 21 + 6 + 14x + 4x2 + -3x2 = -6 + 3x2 + 6 + -3x2 Combine like terms: 21 + 6 = 27 27 + 14x + 4x2 + -3x2 = -6 + 3x2 + 6 + -3x2 Combine like terms: 4x2 + -3x2 = 1x2 27 + 14x + 1x2 = -6 + 3x2 + 6 + -3x2 Reorder the terms: 27 + 14x + 1x2 = -6 + 6 + 3x2 + -3x2 Combine like terms: -6 + 6 = 0 27 + 14x + 1x2 = 0 + 3x2 + -3x2 27 + 14x + 1x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 27 + 14x + 1x2 = 0 Begin completing the square. Move the constant term to the right: Add '-27' to each side of the equation. 27 + 14x + -27 + x2 = 0 + -27 Reorder the terms: 27 + -27 + 14x + x2 = 0 + -27 Combine like terms: 27 + -27 = 0 0 + 14x + x2 = 0 + -27 14x + x2 = 0 + -27 Combine like terms: 0 + -27 = -27 14x + x2 = -27 The x term is 14x. Take half its coefficient (7). Square it (49) and add it to both sides. Add '49' to each side of the equation. 14x + 49 + x2 = -27 + 49 Reorder the terms: 49 + 14x + x2 = -27 + 49 Combine like terms: -27 + 49 = 22 49 + 14x + x2 = 22 Factor a perfect square on the left side: (x + 7)(x + 7) = 22 Calculate the square root of the right side: 4.69041576 Break this problem into two subproblems by setting (x + 7) equal to 4.69041576 and -4.69041576.Subproblem 1
x + 7 = 4.69041576 Simplifying x + 7 = 4.69041576 Reorder the terms: 7 + x = 4.69041576 Solving 7 + x = 4.69041576 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + x = 4.69041576 + -7 Combine like terms: 7 + -7 = 0 0 + x = 4.69041576 + -7 x = 4.69041576 + -7 Combine like terms: 4.69041576 + -7 = -2.30958424 x = -2.30958424 Simplifying x = -2.30958424Subproblem 2
x + 7 = -4.69041576 Simplifying x + 7 = -4.69041576 Reorder the terms: 7 + x = -4.69041576 Solving 7 + x = -4.69041576 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + x = -4.69041576 + -7 Combine like terms: 7 + -7 = 0 0 + x = -4.69041576 + -7 x = -4.69041576 + -7 Combine like terms: -4.69041576 + -7 = -11.69041576 x = -11.69041576 Simplifying x = -11.69041576Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.30958424, -11.69041576}
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