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Simplifying 4x(x + 30) = (5x + -25) Reorder the terms: 4x(30 + x) = (5x + -25) (30 * 4x + x * 4x) = (5x + -25) (120x + 4x2) = (5x + -25) Reorder the terms: 120x + 4x2 = (-25 + 5x) Remove parenthesis around (-25 + 5x) 120x + 4x2 = -25 + 5x Solving 120x + 4x2 = -25 + 5x Solving for variable 'x'. Reorder the terms: 25 + 120x + -5x + 4x2 = -25 + 5x + 25 + -5x Combine like terms: 120x + -5x = 115x 25 + 115x + 4x2 = -25 + 5x + 25 + -5x Reorder the terms: 25 + 115x + 4x2 = -25 + 25 + 5x + -5x Combine like terms: -25 + 25 = 0 25 + 115x + 4x2 = 0 + 5x + -5x 25 + 115x + 4x2 = 5x + -5x Combine like terms: 5x + -5x = 0 25 + 115x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 6.25 + 28.75x + x2 = 0 Move the constant term to the right: Add '-6.25' to each side of the equation. 6.25 + 28.75x + -6.25 + x2 = 0 + -6.25 Reorder the terms: 6.25 + -6.25 + 28.75x + x2 = 0 + -6.25 Combine like terms: 6.25 + -6.25 = 0.00 0.00 + 28.75x + x2 = 0 + -6.25 28.75x + x2 = 0 + -6.25 Combine like terms: 0 + -6.25 = -6.25 28.75x + x2 = -6.25 The x term is 28.75x. Take half its coefficient (14.375). Square it (206.640625) and add it to both sides. Add '206.640625' to each side of the equation. 28.75x + 206.640625 + x2 = -6.25 + 206.640625 Reorder the terms: 206.640625 + 28.75x + x2 = -6.25 + 206.640625 Combine like terms: -6.25 + 206.640625 = 200.390625 206.640625 + 28.75x + x2 = 200.390625 Factor a perfect square on the left side: (x + 14.375)(x + 14.375) = 200.390625 Calculate the square root of the right side: 14.155939566 Break this problem into two subproblems by setting (x + 14.375) equal to 14.155939566 and -14.155939566.Subproblem 1
x + 14.375 = 14.155939566 Simplifying x + 14.375 = 14.155939566 Reorder the terms: 14.375 + x = 14.155939566 Solving 14.375 + x = 14.155939566 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-14.375' to each side of the equation. 14.375 + -14.375 + x = 14.155939566 + -14.375 Combine like terms: 14.375 + -14.375 = 0.000 0.000 + x = 14.155939566 + -14.375 x = 14.155939566 + -14.375 Combine like terms: 14.155939566 + -14.375 = -0.219060434 x = -0.219060434 Simplifying x = -0.219060434Subproblem 2
x + 14.375 = -14.155939566 Simplifying x + 14.375 = -14.155939566 Reorder the terms: 14.375 + x = -14.155939566 Solving 14.375 + x = -14.155939566 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-14.375' to each side of the equation. 14.375 + -14.375 + x = -14.155939566 + -14.375 Combine like terms: 14.375 + -14.375 = 0.000 0.000 + x = -14.155939566 + -14.375 x = -14.155939566 + -14.375 Combine like terms: -14.155939566 + -14.375 = -28.530939566 x = -28.530939566 Simplifying x = -28.530939566Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.219060434, -28.530939566}
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