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Simplifying 5(9x + -1) = 6x(x + 15) Reorder the terms: 5(-1 + 9x) = 6x(x + 15) (-1 * 5 + 9x * 5) = 6x(x + 15) (-5 + 45x) = 6x(x + 15) Reorder the terms: -5 + 45x = 6x(15 + x) -5 + 45x = (15 * 6x + x * 6x) -5 + 45x = (90x + 6x2) Solving -5 + 45x = 90x + 6x2 Solving for variable 'x'. Combine like terms: 45x + -90x = -45x -5 + -45x + -6x2 = 90x + 6x2 + -90x + -6x2 Reorder the terms: -5 + -45x + -6x2 = 90x + -90x + 6x2 + -6x2 Combine like terms: 90x + -90x = 0 -5 + -45x + -6x2 = 0 + 6x2 + -6x2 -5 + -45x + -6x2 = 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 -5 + -45x + -6x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(5 + 45x + 6x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(5 + 45x + 6x2)' equal to zero and attempt to solve: Simplifying 5 + 45x + 6x2 = 0 Solving 5 + 45x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 0.8333333333 + 7.5x + x2 = 0 Move the constant term to the right: Add '-0.8333333333' to each side of the equation. 0.8333333333 + 7.5x + -0.8333333333 + x2 = 0 + -0.8333333333 Reorder the terms: 0.8333333333 + -0.8333333333 + 7.5x + x2 = 0 + -0.8333333333 Combine like terms: 0.8333333333 + -0.8333333333 = 0.0000000000 0.0000000000 + 7.5x + x2 = 0 + -0.8333333333 7.5x + x2 = 0 + -0.8333333333 Combine like terms: 0 + -0.8333333333 = -0.8333333333 7.5x + x2 = -0.8333333333 The x term is 7.5x. Take half its coefficient (3.75). Square it (14.0625) and add it to both sides. Add '14.0625' to each side of the equation. 7.5x + 14.0625 + x2 = -0.8333333333 + 14.0625 Reorder the terms: 14.0625 + 7.5x + x2 = -0.8333333333 + 14.0625 Combine like terms: -0.8333333333 + 14.0625 = 13.2291666667 14.0625 + 7.5x + x2 = 13.2291666667 Factor a perfect square on the left side: (x + 3.75)(x + 3.75) = 13.2291666667 Calculate the square root of the right side: 3.63719214 Break this problem into two subproblems by setting (x + 3.75) equal to 3.63719214 and -3.63719214.Subproblem 1
x + 3.75 = 3.63719214 Simplifying x + 3.75 = 3.63719214 Reorder the terms: 3.75 + x = 3.63719214 Solving 3.75 + x = 3.63719214 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.75' to each side of the equation. 3.75 + -3.75 + x = 3.63719214 + -3.75 Combine like terms: 3.75 + -3.75 = 0.00 0.00 + x = 3.63719214 + -3.75 x = 3.63719214 + -3.75 Combine like terms: 3.63719214 + -3.75 = -0.11280786 x = -0.11280786 Simplifying x = -0.11280786Subproblem 2
x + 3.75 = -3.63719214 Simplifying x + 3.75 = -3.63719214 Reorder the terms: 3.75 + x = -3.63719214 Solving 3.75 + x = -3.63719214 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.75' to each side of the equation. 3.75 + -3.75 + x = -3.63719214 + -3.75 Combine like terms: 3.75 + -3.75 = 0.00 0.00 + x = -3.63719214 + -3.75 x = -3.63719214 + -3.75 Combine like terms: -3.63719214 + -3.75 = -7.38719214 x = -7.38719214 Simplifying x = -7.38719214Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.11280786, -7.38719214}Solution
x = {-0.11280786, -7.38719214}
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