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Simplifying 5x(x + 10) = 3x + 5x + -6 Reorder the terms: 5x(10 + x) = 3x + 5x + -6 (10 * 5x + x * 5x) = 3x + 5x + -6 (50x + 5x2) = 3x + 5x + -6 Reorder the terms: 50x + 5x2 = -6 + 3x + 5x Combine like terms: 3x + 5x = 8x 50x + 5x2 = -6 + 8x Solving 50x + 5x2 = -6 + 8x Solving for variable 'x'. Reorder the terms: 6 + 50x + -8x + 5x2 = -6 + 8x + 6 + -8x Combine like terms: 50x + -8x = 42x 6 + 42x + 5x2 = -6 + 8x + 6 + -8x Reorder the terms: 6 + 42x + 5x2 = -6 + 6 + 8x + -8x Combine like terms: -6 + 6 = 0 6 + 42x + 5x2 = 0 + 8x + -8x 6 + 42x + 5x2 = 8x + -8x Combine like terms: 8x + -8x = 0 6 + 42x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 1.2 + 8.4x + x2 = 0 Move the constant term to the right: Add '-1.2' to each side of the equation. 1.2 + 8.4x + -1.2 + x2 = 0 + -1.2 Reorder the terms: 1.2 + -1.2 + 8.4x + x2 = 0 + -1.2 Combine like terms: 1.2 + -1.2 = 0.0 0.0 + 8.4x + x2 = 0 + -1.2 8.4x + x2 = 0 + -1.2 Combine like terms: 0 + -1.2 = -1.2 8.4x + x2 = -1.2 The x term is 8.4x. Take half its coefficient (4.2). Square it (17.64) and add it to both sides. Add '17.64' to each side of the equation. 8.4x + 17.64 + x2 = -1.2 + 17.64 Reorder the terms: 17.64 + 8.4x + x2 = -1.2 + 17.64 Combine like terms: -1.2 + 17.64 = 16.44 17.64 + 8.4x + x2 = 16.44 Factor a perfect square on the left side: (x + 4.2)(x + 4.2) = 16.44 Calculate the square root of the right side: 4.054626987 Break this problem into two subproblems by setting (x + 4.2) equal to 4.054626987 and -4.054626987.Subproblem 1
x + 4.2 = 4.054626987 Simplifying x + 4.2 = 4.054626987 Reorder the terms: 4.2 + x = 4.054626987 Solving 4.2 + x = 4.054626987 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.2' to each side of the equation. 4.2 + -4.2 + x = 4.054626987 + -4.2 Combine like terms: 4.2 + -4.2 = 0.0 0.0 + x = 4.054626987 + -4.2 x = 4.054626987 + -4.2 Combine like terms: 4.054626987 + -4.2 = -0.145373013 x = -0.145373013 Simplifying x = -0.145373013Subproblem 2
x + 4.2 = -4.054626987 Simplifying x + 4.2 = -4.054626987 Reorder the terms: 4.2 + x = -4.054626987 Solving 4.2 + x = -4.054626987 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.2' to each side of the equation. 4.2 + -4.2 + x = -4.054626987 + -4.2 Combine like terms: 4.2 + -4.2 = 0.0 0.0 + x = -4.054626987 + -4.2 x = -4.054626987 + -4.2 Combine like terms: -4.054626987 + -4.2 = -8.254626987 x = -8.254626987 Simplifying x = -8.254626987Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.145373013, -8.254626987}
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