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Simplifying x(5x + 2) = 75 Reorder the terms: x(2 + 5x) = 75 (2 * x + 5x * x) = 75 (2x + 5x2) = 75 Solving 2x + 5x2 = 75 Solving for variable 'x'. Reorder the terms: -75 + 2x + 5x2 = 75 + -75 Combine like terms: 75 + -75 = 0 -75 + 2x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -15 + 0.4x + x2 = 0 Move the constant term to the right: Add '15' to each side of the equation. -15 + 0.4x + 15 + x2 = 0 + 15 Reorder the terms: -15 + 15 + 0.4x + x2 = 0 + 15 Combine like terms: -15 + 15 = 0 0 + 0.4x + x2 = 0 + 15 0.4x + x2 = 0 + 15 Combine like terms: 0 + 15 = 15 0.4x + x2 = 15 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 = 15 + 0.04 Reorder the terms: 0.04 + 0.4x + x2 = 15 + 0.04 Combine like terms: 15 + 0.04 = 15.04 0.04 + 0.4x + x2 = 15.04 Factor a perfect square on the left side: (x + 0.2)(x + 0.2) = 15.04 Calculate the square root of the right side: 3.878143886 Break this problem into two subproblems by setting (x + 0.2) equal to 3.878143886 and -3.878143886.Subproblem 1
x + 0.2 = 3.878143886 Simplifying x + 0.2 = 3.878143886 Reorder the terms: 0.2 + x = 3.878143886 Solving 0.2 + x = 3.878143886 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 = 3.878143886 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + x = 3.878143886 + -0.2 x = 3.878143886 + -0.2 Combine like terms: 3.878143886 + -0.2 = 3.678143886 x = 3.678143886 Simplifying x = 3.678143886Subproblem 2
x + 0.2 = -3.878143886 Simplifying x + 0.2 = -3.878143886 Reorder the terms: 0.2 + x = -3.878143886 Solving 0.2 + x = -3.878143886 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 = -3.878143886 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + x = -3.878143886 + -0.2 x = -3.878143886 + -0.2 Combine like terms: -3.878143886 + -0.2 = -4.078143886 x = -4.078143886 Simplifying x = -4.078143886Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.678143886, -4.078143886}
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