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Simplifying 5x(x + -6) + 2 = 7x + -6 Reorder the terms: 5x(-6 + x) + 2 = 7x + -6 (-6 * 5x + x * 5x) + 2 = 7x + -6 (-30x + 5x2) + 2 = 7x + -6 Reorder the terms: 2 + -30x + 5x2 = 7x + -6 Reorder the terms: 2 + -30x + 5x2 = -6 + 7x Solving 2 + -30x + 5x2 = -6 + 7x Solving for variable 'x'. Reorder the terms: 2 + 6 + -30x + -7x + 5x2 = -6 + 7x + 6 + -7x Combine like terms: 2 + 6 = 8 8 + -30x + -7x + 5x2 = -6 + 7x + 6 + -7x Combine like terms: -30x + -7x = -37x 8 + -37x + 5x2 = -6 + 7x + 6 + -7x Reorder the terms: 8 + -37x + 5x2 = -6 + 6 + 7x + -7x Combine like terms: -6 + 6 = 0 8 + -37x + 5x2 = 0 + 7x + -7x 8 + -37x + 5x2 = 7x + -7x Combine like terms: 7x + -7x = 0 8 + -37x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 1.6 + -7.4x + x2 = 0 Move the constant term to the right: Add '-1.6' to each side of the equation. 1.6 + -7.4x + -1.6 + x2 = 0 + -1.6 Reorder the terms: 1.6 + -1.6 + -7.4x + x2 = 0 + -1.6 Combine like terms: 1.6 + -1.6 = 0.0 0.0 + -7.4x + x2 = 0 + -1.6 -7.4x + x2 = 0 + -1.6 Combine like terms: 0 + -1.6 = -1.6 -7.4x + x2 = -1.6 The x term is -7.4x. Take half its coefficient (-3.7). Square it (13.69) and add it to both sides. Add '13.69' to each side of the equation. -7.4x + 13.69 + x2 = -1.6 + 13.69 Reorder the terms: 13.69 + -7.4x + x2 = -1.6 + 13.69 Combine like terms: -1.6 + 13.69 = 12.09 13.69 + -7.4x + x2 = 12.09 Factor a perfect square on the left side: (x + -3.7)(x + -3.7) = 12.09 Calculate the square root of the right side: 3.47706773 Break this problem into two subproblems by setting (x + -3.7) equal to 3.47706773 and -3.47706773.Subproblem 1
x + -3.7 = 3.47706773 Simplifying x + -3.7 = 3.47706773 Reorder the terms: -3.7 + x = 3.47706773 Solving -3.7 + x = 3.47706773 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.7' to each side of the equation. -3.7 + 3.7 + x = 3.47706773 + 3.7 Combine like terms: -3.7 + 3.7 = 0.0 0.0 + x = 3.47706773 + 3.7 x = 3.47706773 + 3.7 Combine like terms: 3.47706773 + 3.7 = 7.17706773 x = 7.17706773 Simplifying x = 7.17706773Subproblem 2
x + -3.7 = -3.47706773 Simplifying x + -3.7 = -3.47706773 Reorder the terms: -3.7 + x = -3.47706773 Solving -3.7 + x = -3.47706773 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.7' to each side of the equation. -3.7 + 3.7 + x = -3.47706773 + 3.7 Combine like terms: -3.7 + 3.7 = 0.0 0.0 + x = -3.47706773 + 3.7 x = -3.47706773 + 3.7 Combine like terms: -3.47706773 + 3.7 = 0.22293227 x = 0.22293227 Simplifying x = 0.22293227Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.17706773, 0.22293227}
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