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Simplifying 7x(-8 + 2x) = 4 + -1(3x + -12) (-8 * 7x + 2x * 7x) = 4 + -1(3x + -12) (-56x + 14x2) = 4 + -1(3x + -12) Reorder the terms: -56x + 14x2 = 4 + -1(-12 + 3x) -56x + 14x2 = 4 + (-12 * -1 + 3x * -1) -56x + 14x2 = 4 + (12 + -3x) Combine like terms: 4 + 12 = 16 -56x + 14x2 = 16 + -3x Solving -56x + 14x2 = 16 + -3x Solving for variable 'x'. Reorder the terms: -16 + -56x + 3x + 14x2 = 16 + -3x + -16 + 3x Combine like terms: -56x + 3x = -53x -16 + -53x + 14x2 = 16 + -3x + -16 + 3x Reorder the terms: -16 + -53x + 14x2 = 16 + -16 + -3x + 3x Combine like terms: 16 + -16 = 0 -16 + -53x + 14x2 = 0 + -3x + 3x -16 + -53x + 14x2 = -3x + 3x Combine like terms: -3x + 3x = 0 -16 + -53x + 14x2 = 0 Begin completing the square. Divide all terms by 14 the coefficient of the squared term: Divide each side by '14'. -1.142857143 + -3.785714286x + x2 = 0 Move the constant term to the right: Add '1.142857143' to each side of the equation. -1.142857143 + -3.785714286x + 1.142857143 + x2 = 0 + 1.142857143 Reorder the terms: -1.142857143 + 1.142857143 + -3.785714286x + x2 = 0 + 1.142857143 Combine like terms: -1.142857143 + 1.142857143 = 0.000000000 0.000000000 + -3.785714286x + x2 = 0 + 1.142857143 -3.785714286x + x2 = 0 + 1.142857143 Combine like terms: 0 + 1.142857143 = 1.142857143 -3.785714286x + x2 = 1.142857143 The x term is -3.785714286x. Take half its coefficient (-1.892857143). Square it (3.582908164) and add it to both sides. Add '3.582908164' to each side of the equation. -3.785714286x + 3.582908164 + x2 = 1.142857143 + 3.582908164 Reorder the terms: 3.582908164 + -3.785714286x + x2 = 1.142857143 + 3.582908164 Combine like terms: 1.142857143 + 3.582908164 = 4.725765307 3.582908164 + -3.785714286x + x2 = 4.725765307 Factor a perfect square on the left side: (x + -1.892857143)(x + -1.892857143) = 4.725765307 Calculate the square root of the right side: 2.173882542 Break this problem into two subproblems by setting (x + -1.892857143) equal to 2.173882542 and -2.173882542.Subproblem 1
x + -1.892857143 = 2.173882542 Simplifying x + -1.892857143 = 2.173882542 Reorder the terms: -1.892857143 + x = 2.173882542 Solving -1.892857143 + x = 2.173882542 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.892857143' to each side of the equation. -1.892857143 + 1.892857143 + x = 2.173882542 + 1.892857143 Combine like terms: -1.892857143 + 1.892857143 = 0.000000000 0.000000000 + x = 2.173882542 + 1.892857143 x = 2.173882542 + 1.892857143 Combine like terms: 2.173882542 + 1.892857143 = 4.066739685 x = 4.066739685 Simplifying x = 4.066739685Subproblem 2
x + -1.892857143 = -2.173882542 Simplifying x + -1.892857143 = -2.173882542 Reorder the terms: -1.892857143 + x = -2.173882542 Solving -1.892857143 + x = -2.173882542 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.892857143' to each side of the equation. -1.892857143 + 1.892857143 + x = -2.173882542 + 1.892857143 Combine like terms: -1.892857143 + 1.892857143 = 0.000000000 0.000000000 + x = -2.173882542 + 1.892857143 x = -2.173882542 + 1.892857143 Combine like terms: -2.173882542 + 1.892857143 = -0.281025399 x = -0.281025399 Simplifying x = -0.281025399Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.066739685, -0.281025399}
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