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Simplifying (7x + -4)(5x + 2) = 38 Reorder the terms: (-4 + 7x)(5x + 2) = 38 Reorder the terms: (-4 + 7x)(2 + 5x) = 38 Multiply (-4 + 7x) * (2 + 5x) (-4(2 + 5x) + 7x * (2 + 5x)) = 38 ((2 * -4 + 5x * -4) + 7x * (2 + 5x)) = 38 ((-8 + -20x) + 7x * (2 + 5x)) = 38 (-8 + -20x + (2 * 7x + 5x * 7x)) = 38 (-8 + -20x + (14x + 35x2)) = 38 Combine like terms: -20x + 14x = -6x (-8 + -6x + 35x2) = 38 Solving -8 + -6x + 35x2 = 38 Solving for variable 'x'. Reorder the terms: -8 + -38 + -6x + 35x2 = 38 + -38 Combine like terms: -8 + -38 = -46 -46 + -6x + 35x2 = 38 + -38 Combine like terms: 38 + -38 = 0 -46 + -6x + 35x2 = 0 Begin completing the square. Divide all terms by 35 the coefficient of the squared term: Divide each side by '35'. -1.314285714 + -0.1714285714x + x2 = 0 Move the constant term to the right: Add '1.314285714' to each side of the equation. -1.314285714 + -0.1714285714x + 1.314285714 + x2 = 0 + 1.314285714 Reorder the terms: -1.314285714 + 1.314285714 + -0.1714285714x + x2 = 0 + 1.314285714 Combine like terms: -1.314285714 + 1.314285714 = 0.000000000 0.000000000 + -0.1714285714x + x2 = 0 + 1.314285714 -0.1714285714x + x2 = 0 + 1.314285714 Combine like terms: 0 + 1.314285714 = 1.314285714 -0.1714285714x + x2 = 1.314285714 The x term is -0.1714285714x. Take half its coefficient (-0.0857142857). Square it (0.007346938773) and add it to both sides. Add '0.007346938773' to each side of the equation. -0.1714285714x + 0.007346938773 + x2 = 1.314285714 + 0.007346938773 Reorder the terms: 0.007346938773 + -0.1714285714x + x2 = 1.314285714 + 0.007346938773 Combine like terms: 1.314285714 + 0.007346938773 = 1.321632652773 0.007346938773 + -0.1714285714x + x2 = 1.321632652773 Factor a perfect square on the left side: (x + -0.0857142857)(x + -0.0857142857) = 1.321632652773 Calculate the square root of the right side: 1.149622831 Break this problem into two subproblems by setting (x + -0.0857142857) equal to 1.149622831 and -1.149622831.Subproblem 1
x + -0.0857142857 = 1.149622831 Simplifying x + -0.0857142857 = 1.149622831 Reorder the terms: -0.0857142857 + x = 1.149622831 Solving -0.0857142857 + x = 1.149622831 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.0857142857' to each side of the equation. -0.0857142857 + 0.0857142857 + x = 1.149622831 + 0.0857142857 Combine like terms: -0.0857142857 + 0.0857142857 = 0.0000000000 0.0000000000 + x = 1.149622831 + 0.0857142857 x = 1.149622831 + 0.0857142857 Combine like terms: 1.149622831 + 0.0857142857 = 1.2353371167 x = 1.2353371167 Simplifying x = 1.2353371167Subproblem 2
x + -0.0857142857 = -1.149622831 Simplifying x + -0.0857142857 = -1.149622831 Reorder the terms: -0.0857142857 + x = -1.149622831 Solving -0.0857142857 + x = -1.149622831 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.0857142857' to each side of the equation. -0.0857142857 + 0.0857142857 + x = -1.149622831 + 0.0857142857 Combine like terms: -0.0857142857 + 0.0857142857 = 0.0000000000 0.0000000000 + x = -1.149622831 + 0.0857142857 x = -1.149622831 + 0.0857142857 Combine like terms: -1.149622831 + 0.0857142857 = -1.0639085453 x = -1.0639085453 Simplifying x = -1.0639085453Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.2353371167, -1.0639085453}
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