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Simplifying 2x + 2x(5x + -3) = 85 Reorder the terms: 2x + 2x(-3 + 5x) = 85 2x + (-3 * 2x + 5x * 2x) = 85 2x + (-6x + 10x2) = 85 Combine like terms: 2x + -6x = -4x -4x + 10x2 = 85 Solving -4x + 10x2 = 85 Solving for variable 'x'. Reorder the terms: -85 + -4x + 10x2 = 85 + -85 Combine like terms: 85 + -85 = 0 -85 + -4x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -8.5 + -0.4x + x2 = 0.0 Move the constant term to the right: Add '8.5' to each side of the equation. -8.5 + -0.4x + 8.5 + x2 = 0.0 + 8.5 Reorder the terms: -8.5 + 8.5 + -0.4x + x2 = 0.0 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + -0.4x + x2 = 0.0 + 8.5 -0.4x + x2 = 0.0 + 8.5 Combine like terms: 0.0 + 8.5 = 8.5 -0.4x + x2 = 8.5 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 = 8.5 + 0.04 Reorder the terms: 0.04 + -0.4x + x2 = 8.5 + 0.04 Combine like terms: 8.5 + 0.04 = 8.54 0.04 + -0.4x + x2 = 8.54 Factor a perfect square on the left side: (x + -0.2)(x + -0.2) = 8.54 Calculate the square root of the right side: 2.922327839 Break this problem into two subproblems by setting (x + -0.2) equal to 2.922327839 and -2.922327839.Subproblem 1
x + -0.2 = 2.922327839 Simplifying x + -0.2 = 2.922327839 Reorder the terms: -0.2 + x = 2.922327839 Solving -0.2 + x = 2.922327839 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 = 2.922327839 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + x = 2.922327839 + 0.2 x = 2.922327839 + 0.2 Combine like terms: 2.922327839 + 0.2 = 3.122327839 x = 3.122327839 Simplifying x = 3.122327839Subproblem 2
x + -0.2 = -2.922327839 Simplifying x + -0.2 = -2.922327839 Reorder the terms: -0.2 + x = -2.922327839 Solving -0.2 + x = -2.922327839 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 = -2.922327839 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + x = -2.922327839 + 0.2 x = -2.922327839 + 0.2 Combine like terms: -2.922327839 + 0.2 = -2.722327839 x = -2.722327839 Simplifying x = -2.722327839Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.122327839, -2.722327839}
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