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Simplifying 5x(x + -6) + -7(x + 2) = -10 Reorder the terms: 5x(-6 + x) + -7(x + 2) = -10 (-6 * 5x + x * 5x) + -7(x + 2) = -10 (-30x + 5x2) + -7(x + 2) = -10 Reorder the terms: -30x + 5x2 + -7(2 + x) = -10 -30x + 5x2 + (2 * -7 + x * -7) = -10 -30x + 5x2 + (-14 + -7x) = -10 Reorder the terms: -14 + -30x + -7x + 5x2 = -10 Combine like terms: -30x + -7x = -37x -14 + -37x + 5x2 = -10 Solving -14 + -37x + 5x2 = -10 Solving for variable 'x'. Reorder the terms: -14 + 10 + -37x + 5x2 = -10 + 10 Combine like terms: -14 + 10 = -4 -4 + -37x + 5x2 = -10 + 10 Combine like terms: -10 + 10 = 0 -4 + -37x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -0.8 + -7.4x + x2 = 0 Move the constant term to the right: Add '0.8' to each side of the equation. -0.8 + -7.4x + 0.8 + x2 = 0 + 0.8 Reorder the terms: -0.8 + 0.8 + -7.4x + x2 = 0 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + -7.4x + x2 = 0 + 0.8 -7.4x + x2 = 0 + 0.8 Combine like terms: 0 + 0.8 = 0.8 -7.4x + x2 = 0.8 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 = 0.8 + 13.69 Reorder the terms: 13.69 + -7.4x + x2 = 0.8 + 13.69 Combine like terms: 0.8 + 13.69 = 14.49 13.69 + -7.4x + x2 = 14.49 Factor a perfect square on the left side: (x + -3.7)(x + -3.7) = 14.49 Calculate the square root of the right side: 3.806573262 Break this problem into two subproblems by setting (x + -3.7) equal to 3.806573262 and -3.806573262.Subproblem 1
x + -3.7 = 3.806573262 Simplifying x + -3.7 = 3.806573262 Reorder the terms: -3.7 + x = 3.806573262 Solving -3.7 + x = 3.806573262 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 = 3.806573262 + 3.7 Combine like terms: -3.7 + 3.7 = 0.0 0.0 + x = 3.806573262 + 3.7 x = 3.806573262 + 3.7 Combine like terms: 3.806573262 + 3.7 = 7.506573262 x = 7.506573262 Simplifying x = 7.506573262Subproblem 2
x + -3.7 = -3.806573262 Simplifying x + -3.7 = -3.806573262 Reorder the terms: -3.7 + x = -3.806573262 Solving -3.7 + x = -3.806573262 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 = -3.806573262 + 3.7 Combine like terms: -3.7 + 3.7 = 0.0 0.0 + x = -3.806573262 + 3.7 x = -3.806573262 + 3.7 Combine like terms: -3.806573262 + 3.7 = -0.106573262 x = -0.106573262 Simplifying x = -0.106573262Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.506573262, -0.106573262}
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