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Simplifying 115 = 2x(5x + -2) Reorder the terms: 115 = 2x(-2 + 5x) 115 = (-2 * 2x + 5x * 2x) 115 = (-4x + 10x2) Solving 115 = -4x + 10x2 Solving for variable 'x'. Reorder the terms: 115 + 4x + -10x2 = -4x + 4x + 10x2 + -10x2 Combine like terms: -4x + 4x = 0 115 + 4x + -10x2 = 0 + 10x2 + -10x2 115 + 4x + -10x2 = 10x2 + -10x2 Combine like terms: 10x2 + -10x2 = 0 115 + 4x + -10x2 = 0 Begin completing the square. Divide all terms by -10 the coefficient of the squared term: Divide each side by '-10'. -11.5 + -0.4x + x2 = 0 Move the constant term to the right: Add '11.5' to each side of the equation. -11.5 + -0.4x + 11.5 + x2 = 0 + 11.5 Reorder the terms: -11.5 + 11.5 + -0.4x + x2 = 0 + 11.5 Combine like terms: -11.5 + 11.5 = 0.0 0.0 + -0.4x + x2 = 0 + 11.5 -0.4x + x2 = 0 + 11.5 Combine like terms: 0 + 11.5 = 11.5 -0.4x + x2 = 11.5 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 = 11.5 + 0.04 Reorder the terms: 0.04 + -0.4x + x2 = 11.5 + 0.04 Combine like terms: 11.5 + 0.04 = 11.54 0.04 + -0.4x + x2 = 11.54 Factor a perfect square on the left side: (x + -0.2)(x + -0.2) = 11.54 Calculate the square root of the right side: 3.39705755 Break this problem into two subproblems by setting (x + -0.2) equal to 3.39705755 and -3.39705755.Subproblem 1
x + -0.2 = 3.39705755 Simplifying x + -0.2 = 3.39705755 Reorder the terms: -0.2 + x = 3.39705755 Solving -0.2 + x = 3.39705755 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 = 3.39705755 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + x = 3.39705755 + 0.2 x = 3.39705755 + 0.2 Combine like terms: 3.39705755 + 0.2 = 3.59705755 x = 3.59705755 Simplifying x = 3.59705755Subproblem 2
x + -0.2 = -3.39705755 Simplifying x + -0.2 = -3.39705755 Reorder the terms: -0.2 + x = -3.39705755 Solving -0.2 + x = -3.39705755 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 = -3.39705755 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + x = -3.39705755 + 0.2 x = -3.39705755 + 0.2 Combine like terms: -3.39705755 + 0.2 = -3.19705755 x = -3.19705755 Simplifying x = -3.19705755Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.59705755, -3.19705755}
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