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Simplifying ((x + -6) * 2 + 5x2) + -36 = 0 Reorder the terms: ((-6 + x) * 2 + 5x2) + -36 = 0 Reorder the terms for easier multiplication: (2(-6 + x) + 5x2) + -36 = 0 ((-6 * 2 + x * 2) + 5x2) + -36 = 0 ((-12 + 2x) + 5x2) + -36 = 0 Remove parenthesis around (-12 + 2x + 5x2) -12 + 2x + 5x2 + -36 = 0 Reorder the terms: -12 + -36 + 2x + 5x2 = 0 Combine like terms: -12 + -36 = -48 -48 + 2x + 5x2 = 0 Solving -48 + 2x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -9.6 + 0.4x + x2 = 0 Move the constant term to the right: Add '9.6' to each side of the equation. -9.6 + 0.4x + 9.6 + x2 = 0 + 9.6 Reorder the terms: -9.6 + 9.6 + 0.4x + x2 = 0 + 9.6 Combine like terms: -9.6 + 9.6 = 0.0 0.0 + 0.4x + x2 = 0 + 9.6 0.4x + x2 = 0 + 9.6 Combine like terms: 0 + 9.6 = 9.6 0.4x + x2 = 9.6 The x term is 0.4x. Take half its coefficient (0.2). Square it (0.04) and add it to both sides. Add '0.04' to each side of the equation. 0.4x + 0.04 + x2 = 9.6 + 0.04 Reorder the terms: 0.04 + 0.4x + x2 = 9.6 + 0.04 Combine like terms: 9.6 + 0.04 = 9.64 0.04 + 0.4x + x2 = 9.64 Factor a perfect square on the left side: (x + 0.2)(x + 0.2) = 9.64 Calculate the square root of the right side: 3.104834939 Break this problem into two subproblems by setting (x + 0.2) equal to 3.104834939 and -3.104834939.Subproblem 1
x + 0.2 = 3.104834939 Simplifying x + 0.2 = 3.104834939 Reorder the terms: 0.2 + x = 3.104834939 Solving 0.2 + x = 3.104834939 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2' to each side of the equation. 0.2 + -0.2 + x = 3.104834939 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + x = 3.104834939 + -0.2 x = 3.104834939 + -0.2 Combine like terms: 3.104834939 + -0.2 = 2.904834939 x = 2.904834939 Simplifying x = 2.904834939Subproblem 2
x + 0.2 = -3.104834939 Simplifying x + 0.2 = -3.104834939 Reorder the terms: 0.2 + x = -3.104834939 Solving 0.2 + x = -3.104834939 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2' to each side of the equation. 0.2 + -0.2 + x = -3.104834939 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + x = -3.104834939 + -0.2 x = -3.104834939 + -0.2 Combine like terms: -3.104834939 + -0.2 = -3.304834939 x = -3.304834939 Simplifying x = -3.304834939Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.904834939, -3.304834939}
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