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Simplifying 5x(x + -6) + -2 = 2x + -5 Reorder the terms: 5x(-6 + x) + -2 = 2x + -5 (-6 * 5x + x * 5x) + -2 = 2x + -5 (-30x + 5x2) + -2 = 2x + -5 Reorder the terms: -2 + -30x + 5x2 = 2x + -5 Reorder the terms: -2 + -30x + 5x2 = -5 + 2x Solving -2 + -30x + 5x2 = -5 + 2x Solving for variable 'x'. Reorder the terms: -2 + 5 + -30x + -2x + 5x2 = -5 + 2x + 5 + -2x Combine like terms: -2 + 5 = 3 3 + -30x + -2x + 5x2 = -5 + 2x + 5 + -2x Combine like terms: -30x + -2x = -32x 3 + -32x + 5x2 = -5 + 2x + 5 + -2x Reorder the terms: 3 + -32x + 5x2 = -5 + 5 + 2x + -2x Combine like terms: -5 + 5 = 0 3 + -32x + 5x2 = 0 + 2x + -2x 3 + -32x + 5x2 = 2x + -2x Combine like terms: 2x + -2x = 0 3 + -32x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 0.6 + -6.4x + x2 = 0 Move the constant term to the right: Add '-0.6' to each side of the equation. 0.6 + -6.4x + -0.6 + x2 = 0 + -0.6 Reorder the terms: 0.6 + -0.6 + -6.4x + x2 = 0 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + -6.4x + x2 = 0 + -0.6 -6.4x + x2 = 0 + -0.6 Combine like terms: 0 + -0.6 = -0.6 -6.4x + x2 = -0.6 The x term is -6.4x. Take half its coefficient (-3.2). Square it (10.24) and add it to both sides. Add '10.24' to each side of the equation. -6.4x + 10.24 + x2 = -0.6 + 10.24 Reorder the terms: 10.24 + -6.4x + x2 = -0.6 + 10.24 Combine like terms: -0.6 + 10.24 = 9.64 10.24 + -6.4x + x2 = 9.64 Factor a perfect square on the left side: (x + -3.2)(x + -3.2) = 9.64 Calculate the square root of the right side: 3.104834939 Break this problem into two subproblems by setting (x + -3.2) equal to 3.104834939 and -3.104834939.Subproblem 1
x + -3.2 = 3.104834939 Simplifying x + -3.2 = 3.104834939 Reorder the terms: -3.2 + x = 3.104834939 Solving -3.2 + x = 3.104834939 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.2' to each side of the equation. -3.2 + 3.2 + x = 3.104834939 + 3.2 Combine like terms: -3.2 + 3.2 = 0.0 0.0 + x = 3.104834939 + 3.2 x = 3.104834939 + 3.2 Combine like terms: 3.104834939 + 3.2 = 6.304834939 x = 6.304834939 Simplifying x = 6.304834939Subproblem 2
x + -3.2 = -3.104834939 Simplifying x + -3.2 = -3.104834939 Reorder the terms: -3.2 + x = -3.104834939 Solving -3.2 + x = -3.104834939 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.2' to each side of the equation. -3.2 + 3.2 + x = -3.104834939 + 3.2 Combine like terms: -3.2 + 3.2 = 0.0 0.0 + x = -3.104834939 + 3.2 x = -3.104834939 + 3.2 Combine like terms: -3.104834939 + 3.2 = 0.095165061 x = 0.095165061 Simplifying x = 0.095165061Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.304834939, 0.095165061}
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