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Simplifying (7x + -28)(10x + -13) = 180 Reorder the terms: (-28 + 7x)(10x + -13) = 180 Reorder the terms: (-28 + 7x)(-13 + 10x) = 180 Multiply (-28 + 7x) * (-13 + 10x) (-28(-13 + 10x) + 7x * (-13 + 10x)) = 180 ((-13 * -28 + 10x * -28) + 7x * (-13 + 10x)) = 180 ((364 + -280x) + 7x * (-13 + 10x)) = 180 (364 + -280x + (-13 * 7x + 10x * 7x)) = 180 (364 + -280x + (-91x + 70x2)) = 180 Combine like terms: -280x + -91x = -371x (364 + -371x + 70x2) = 180 Solving 364 + -371x + 70x2 = 180 Solving for variable 'x'. Reorder the terms: 364 + -180 + -371x + 70x2 = 180 + -180 Combine like terms: 364 + -180 = 184 184 + -371x + 70x2 = 180 + -180 Combine like terms: 180 + -180 = 0 184 + -371x + 70x2 = 0 Begin completing the square. Divide all terms by 70 the coefficient of the squared term: Divide each side by '70'. 2.628571429 + -5.3x + x2 = 0.0 Move the constant term to the right: Add '-2.628571429' to each side of the equation. 2.628571429 + -5.3x + -2.628571429 + x2 = 0.0 + -2.628571429 Reorder the terms: 2.628571429 + -2.628571429 + -5.3x + x2 = 0.0 + -2.628571429 Combine like terms: 2.628571429 + -2.628571429 = 0.000000000 0.000000000 + -5.3x + x2 = 0.0 + -2.628571429 -5.3x + x2 = 0.0 + -2.628571429 Combine like terms: 0.0 + -2.628571429 = -2.628571429 -5.3x + x2 = -2.628571429 The x term is -5.3x. Take half its coefficient (-2.65). Square it (7.0225) and add it to both sides. Add '7.0225' to each side of the equation. -5.3x + 7.0225 + x2 = -2.628571429 + 7.0225 Reorder the terms: 7.0225 + -5.3x + x2 = -2.628571429 + 7.0225 Combine like terms: -2.628571429 + 7.0225 = 4.393928571 7.0225 + -5.3x + x2 = 4.393928571 Factor a perfect square on the left side: (x + -2.65)(x + -2.65) = 4.393928571 Calculate the square root of the right side: 2.096169977 Break this problem into two subproblems by setting (x + -2.65) equal to 2.096169977 and -2.096169977.Subproblem 1
x + -2.65 = 2.096169977 Simplifying x + -2.65 = 2.096169977 Reorder the terms: -2.65 + x = 2.096169977 Solving -2.65 + x = 2.096169977 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.65' to each side of the equation. -2.65 + 2.65 + x = 2.096169977 + 2.65 Combine like terms: -2.65 + 2.65 = 0.00 0.00 + x = 2.096169977 + 2.65 x = 2.096169977 + 2.65 Combine like terms: 2.096169977 + 2.65 = 4.746169977 x = 4.746169977 Simplifying x = 4.746169977Subproblem 2
x + -2.65 = -2.096169977 Simplifying x + -2.65 = -2.096169977 Reorder the terms: -2.65 + x = -2.096169977 Solving -2.65 + x = -2.096169977 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.65' to each side of the equation. -2.65 + 2.65 + x = -2.096169977 + 2.65 Combine like terms: -2.65 + 2.65 = 0.00 0.00 + x = -2.096169977 + 2.65 x = -2.096169977 + 2.65 Combine like terms: -2.096169977 + 2.65 = 0.553830023 x = 0.553830023 Simplifying x = 0.553830023Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.746169977, 0.553830023}
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