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Simplifying (5x + 25)(x + 30) = 4x Reorder the terms: (25 + 5x)(x + 30) = 4x Reorder the terms: (25 + 5x)(30 + x) = 4x Multiply (25 + 5x) * (30 + x) (25(30 + x) + 5x * (30 + x)) = 4x ((30 * 25 + x * 25) + 5x * (30 + x)) = 4x ((750 + 25x) + 5x * (30 + x)) = 4x (750 + 25x + (30 * 5x + x * 5x)) = 4x (750 + 25x + (150x + 5x2)) = 4x Combine like terms: 25x + 150x = 175x (750 + 175x + 5x2) = 4x Solving 750 + 175x + 5x2 = 4x Solving for variable 'x'. Reorder the terms: 750 + 175x + -4x + 5x2 = 4x + -4x Combine like terms: 175x + -4x = 171x 750 + 171x + 5x2 = 4x + -4x Combine like terms: 4x + -4x = 0 750 + 171x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 150 + 34.2x + x2 = 0 Move the constant term to the right: Add '-150' to each side of the equation. 150 + 34.2x + -150 + x2 = 0 + -150 Reorder the terms: 150 + -150 + 34.2x + x2 = 0 + -150 Combine like terms: 150 + -150 = 0 0 + 34.2x + x2 = 0 + -150 34.2x + x2 = 0 + -150 Combine like terms: 0 + -150 = -150 34.2x + x2 = -150 The x term is 34.2x. Take half its coefficient (17.1). Square it (292.41) and add it to both sides. Add '292.41' to each side of the equation. 34.2x + 292.41 + x2 = -150 + 292.41 Reorder the terms: 292.41 + 34.2x + x2 = -150 + 292.41 Combine like terms: -150 + 292.41 = 142.41 292.41 + 34.2x + x2 = 142.41 Factor a perfect square on the left side: (x + 17.1)(x + 17.1) = 142.41 Calculate the square root of the right side: 11.933566106 Break this problem into two subproblems by setting (x + 17.1) equal to 11.933566106 and -11.933566106.Subproblem 1
x + 17.1 = 11.933566106 Simplifying x + 17.1 = 11.933566106 Reorder the terms: 17.1 + x = 11.933566106 Solving 17.1 + x = 11.933566106 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-17.1' to each side of the equation. 17.1 + -17.1 + x = 11.933566106 + -17.1 Combine like terms: 17.1 + -17.1 = 0.0 0.0 + x = 11.933566106 + -17.1 x = 11.933566106 + -17.1 Combine like terms: 11.933566106 + -17.1 = -5.166433894 x = -5.166433894 Simplifying x = -5.166433894Subproblem 2
x + 17.1 = -11.933566106 Simplifying x + 17.1 = -11.933566106 Reorder the terms: 17.1 + x = -11.933566106 Solving 17.1 + x = -11.933566106 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-17.1' to each side of the equation. 17.1 + -17.1 + x = -11.933566106 + -17.1 Combine like terms: 17.1 + -17.1 = 0.0 0.0 + x = -11.933566106 + -17.1 x = -11.933566106 + -17.1 Combine like terms: -11.933566106 + -17.1 = -29.033566106 x = -29.033566106 Simplifying x = -29.033566106Solution
The solution to the problem is based on the solutions from the subproblems. x = {-5.166433894, -29.033566106}
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