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Simplifying (3x + 8)(7x + -28) = 180 Reorder the terms: (8 + 3x)(7x + -28) = 180 Reorder the terms: (8 + 3x)(-28 + 7x) = 180 Multiply (8 + 3x) * (-28 + 7x) (8(-28 + 7x) + 3x * (-28 + 7x)) = 180 ((-28 * 8 + 7x * 8) + 3x * (-28 + 7x)) = 180 ((-224 + 56x) + 3x * (-28 + 7x)) = 180 (-224 + 56x + (-28 * 3x + 7x * 3x)) = 180 (-224 + 56x + (-84x + 21x2)) = 180 Combine like terms: 56x + -84x = -28x (-224 + -28x + 21x2) = 180 Solving -224 + -28x + 21x2 = 180 Solving for variable 'x'. Reorder the terms: -224 + -180 + -28x + 21x2 = 180 + -180 Combine like terms: -224 + -180 = -404 -404 + -28x + 21x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -404 + -28x + 21x2 = 0 Begin completing the square. Divide all terms by 21 the coefficient of the squared term: Divide each side by '21'. -19.23809524 + -1.333333333x + x2 = 0 Move the constant term to the right: Add '19.23809524' to each side of the equation. -19.23809524 + -1.333333333x + 19.23809524 + x2 = 0 + 19.23809524 Reorder the terms: -19.23809524 + 19.23809524 + -1.333333333x + x2 = 0 + 19.23809524 Combine like terms: -19.23809524 + 19.23809524 = 0.00000000 0.00000000 + -1.333333333x + x2 = 0 + 19.23809524 -1.333333333x + x2 = 0 + 19.23809524 Combine like terms: 0 + 19.23809524 = 19.23809524 -1.333333333x + x2 = 19.23809524 The x term is -1.333333333x. Take half its coefficient (-0.6666666665). Square it (0.4444444442) and add it to both sides. Add '0.4444444442' to each side of the equation. -1.333333333x + 0.4444444442 + x2 = 19.23809524 + 0.4444444442 Reorder the terms: 0.4444444442 + -1.333333333x + x2 = 19.23809524 + 0.4444444442 Combine like terms: 19.23809524 + 0.4444444442 = 19.6825396842 0.4444444442 + -1.333333333x + x2 = 19.6825396842 Factor a perfect square on the left side: (x + -0.6666666665)(x + -0.6666666665) = 19.6825396842 Calculate the square root of the right side: 4.436500838 Break this problem into two subproblems by setting (x + -0.6666666665) equal to 4.436500838 and -4.436500838.Subproblem 1
x + -0.6666666665 = 4.436500838 Simplifying x + -0.6666666665 = 4.436500838 Reorder the terms: -0.6666666665 + x = 4.436500838 Solving -0.6666666665 + x = 4.436500838 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6666666665' to each side of the equation. -0.6666666665 + 0.6666666665 + x = 4.436500838 + 0.6666666665 Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000 0.0000000000 + x = 4.436500838 + 0.6666666665 x = 4.436500838 + 0.6666666665 Combine like terms: 4.436500838 + 0.6666666665 = 5.1031675045 x = 5.1031675045 Simplifying x = 5.1031675045Subproblem 2
x + -0.6666666665 = -4.436500838 Simplifying x + -0.6666666665 = -4.436500838 Reorder the terms: -0.6666666665 + x = -4.436500838 Solving -0.6666666665 + x = -4.436500838 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6666666665' to each side of the equation. -0.6666666665 + 0.6666666665 + x = -4.436500838 + 0.6666666665 Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000 0.0000000000 + x = -4.436500838 + 0.6666666665 x = -4.436500838 + 0.6666666665 Combine like terms: -4.436500838 + 0.6666666665 = -3.7698341715 x = -3.7698341715 Simplifying x = -3.7698341715Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.1031675045, -3.7698341715}
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