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Simplifying (5x + -1)(2x + -4) = 7x Reorder the terms: (-1 + 5x)(2x + -4) = 7x Reorder the terms: (-1 + 5x)(-4 + 2x) = 7x Multiply (-1 + 5x) * (-4 + 2x) (-1(-4 + 2x) + 5x * (-4 + 2x)) = 7x ((-4 * -1 + 2x * -1) + 5x * (-4 + 2x)) = 7x ((4 + -2x) + 5x * (-4 + 2x)) = 7x (4 + -2x + (-4 * 5x + 2x * 5x)) = 7x (4 + -2x + (-20x + 10x2)) = 7x Combine like terms: -2x + -20x = -22x (4 + -22x + 10x2) = 7x Solving 4 + -22x + 10x2 = 7x Solving for variable 'x'. Reorder the terms: 4 + -22x + -7x + 10x2 = 7x + -7x Combine like terms: -22x + -7x = -29x 4 + -29x + 10x2 = 7x + -7x Combine like terms: 7x + -7x = 0 4 + -29x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. 0.4 + -2.9x + x2 = 0.0 Move the constant term to the right: Add '-0.4' to each side of the equation. 0.4 + -2.9x + -0.4 + x2 = 0.0 + -0.4 Reorder the terms: 0.4 + -0.4 + -2.9x + x2 = 0.0 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + -2.9x + x2 = 0.0 + -0.4 -2.9x + x2 = 0.0 + -0.4 Combine like terms: 0.0 + -0.4 = -0.4 -2.9x + x2 = -0.4 The x term is -2.9x. Take half its coefficient (-1.45). Square it (2.1025) and add it to both sides. Add '2.1025' to each side of the equation. -2.9x + 2.1025 + x2 = -0.4 + 2.1025 Reorder the terms: 2.1025 + -2.9x + x2 = -0.4 + 2.1025 Combine like terms: -0.4 + 2.1025 = 1.7025 2.1025 + -2.9x + x2 = 1.7025 Factor a perfect square on the left side: (x + -1.45)(x + -1.45) = 1.7025 Calculate the square root of the right side: 1.304798835 Break this problem into two subproblems by setting (x + -1.45) equal to 1.304798835 and -1.304798835.Subproblem 1
x + -1.45 = 1.304798835 Simplifying x + -1.45 = 1.304798835 Reorder the terms: -1.45 + x = 1.304798835 Solving -1.45 + x = 1.304798835 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.45' to each side of the equation. -1.45 + 1.45 + x = 1.304798835 + 1.45 Combine like terms: -1.45 + 1.45 = 0.00 0.00 + x = 1.304798835 + 1.45 x = 1.304798835 + 1.45 Combine like terms: 1.304798835 + 1.45 = 2.754798835 x = 2.754798835 Simplifying x = 2.754798835Subproblem 2
x + -1.45 = -1.304798835 Simplifying x + -1.45 = -1.304798835 Reorder the terms: -1.45 + x = -1.304798835 Solving -1.45 + x = -1.304798835 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.45' to each side of the equation. -1.45 + 1.45 + x = -1.304798835 + 1.45 Combine like terms: -1.45 + 1.45 = 0.00 0.00 + x = -1.304798835 + 1.45 x = -1.304798835 + 1.45 Combine like terms: -1.304798835 + 1.45 = 0.145201165 x = 0.145201165 Simplifying x = 0.145201165Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.754798835, 0.145201165}
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