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Simplifying 5x2 + 2x + -375 = 0 Reorder the terms: -375 + 2x + 5x2 = 0 Solving -375 + 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'. -75 + 0.4x + x2 = 0 Move the constant term to the right: Add '75' to each side of the equation. -75 + 0.4x + 75 + x2 = 0 + 75 Reorder the terms: -75 + 75 + 0.4x + x2 = 0 + 75 Combine like terms: -75 + 75 = 0 0 + 0.4x + x2 = 0 + 75 0.4x + x2 = 0 + 75 Combine like terms: 0 + 75 = 75 0.4x + x2 = 75 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 = 75 + 0.04 Reorder the terms: 0.04 + 0.4x + x2 = 75 + 0.04 Combine like terms: 75 + 0.04 = 75.04 0.04 + 0.4x + x2 = 75.04 Factor a perfect square on the left side: (x + 0.2)(x + 0.2) = 75.04 Calculate the square root of the right side: 8.662563131 Break this problem into two subproblems by setting (x + 0.2) equal to 8.662563131 and -8.662563131.Subproblem 1
x + 0.2 = 8.662563131 Simplifying x + 0.2 = 8.662563131 Reorder the terms: 0.2 + x = 8.662563131 Solving 0.2 + x = 8.662563131 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 = 8.662563131 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + x = 8.662563131 + -0.2 x = 8.662563131 + -0.2 Combine like terms: 8.662563131 + -0.2 = 8.462563131 x = 8.462563131 Simplifying x = 8.462563131Subproblem 2
x + 0.2 = -8.662563131 Simplifying x + 0.2 = -8.662563131 Reorder the terms: 0.2 + x = -8.662563131 Solving 0.2 + x = -8.662563131 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 = -8.662563131 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + x = -8.662563131 + -0.2 x = -8.662563131 + -0.2 Combine like terms: -8.662563131 + -0.2 = -8.862563131 x = -8.862563131 Simplifying x = -8.862563131Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.462563131, -8.862563131}
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