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Simplifying 4x(x + -5) = -25 + 6x Reorder the terms: 4x(-5 + x) = -25 + 6x (-5 * 4x + x * 4x) = -25 + 6x (-20x + 4x2) = -25 + 6x Solving -20x + 4x2 = -25 + 6x Solving for variable 'x'. Reorder the terms: 25 + -20x + -6x + 4x2 = -25 + 6x + 25 + -6x Combine like terms: -20x + -6x = -26x 25 + -26x + 4x2 = -25 + 6x + 25 + -6x Reorder the terms: 25 + -26x + 4x2 = -25 + 25 + 6x + -6x Combine like terms: -25 + 25 = 0 25 + -26x + 4x2 = 0 + 6x + -6x 25 + -26x + 4x2 = 6x + -6x Combine like terms: 6x + -6x = 0 25 + -26x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 6.25 + -6.5x + x2 = 0 Move the constant term to the right: Add '-6.25' to each side of the equation. 6.25 + -6.5x + -6.25 + x2 = 0 + -6.25 Reorder the terms: 6.25 + -6.25 + -6.5x + x2 = 0 + -6.25 Combine like terms: 6.25 + -6.25 = 0.00 0.00 + -6.5x + x2 = 0 + -6.25 -6.5x + x2 = 0 + -6.25 Combine like terms: 0 + -6.25 = -6.25 -6.5x + x2 = -6.25 The x term is -6.5x. Take half its coefficient (-3.25). Square it (10.5625) and add it to both sides. Add '10.5625' to each side of the equation. -6.5x + 10.5625 + x2 = -6.25 + 10.5625 Reorder the terms: 10.5625 + -6.5x + x2 = -6.25 + 10.5625 Combine like terms: -6.25 + 10.5625 = 4.3125 10.5625 + -6.5x + x2 = 4.3125 Factor a perfect square on the left side: (x + -3.25)(x + -3.25) = 4.3125 Calculate the square root of the right side: 2.076655966 Break this problem into two subproblems by setting (x + -3.25) equal to 2.076655966 and -2.076655966.Subproblem 1
x + -3.25 = 2.076655966 Simplifying x + -3.25 = 2.076655966 Reorder the terms: -3.25 + x = 2.076655966 Solving -3.25 + x = 2.076655966 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.25' to each side of the equation. -3.25 + 3.25 + x = 2.076655966 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + x = 2.076655966 + 3.25 x = 2.076655966 + 3.25 Combine like terms: 2.076655966 + 3.25 = 5.326655966 x = 5.326655966 Simplifying x = 5.326655966Subproblem 2
x + -3.25 = -2.076655966 Simplifying x + -3.25 = -2.076655966 Reorder the terms: -3.25 + x = -2.076655966 Solving -3.25 + x = -2.076655966 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.25' to each side of the equation. -3.25 + 3.25 + x = -2.076655966 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + x = -2.076655966 + 3.25 x = -2.076655966 + 3.25 Combine like terms: -2.076655966 + 3.25 = 1.173344034 x = 1.173344034 Simplifying x = 1.173344034Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.326655966, 1.173344034}
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