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Simplifying 5x2 + 3x + -190 = 0 Reorder the terms: -190 + 3x + 5x2 = 0 Solving -190 + 3x + 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'. -38 + 0.6x + x2 = 0 Move the constant term to the right: Add '38' to each side of the equation. -38 + 0.6x + 38 + x2 = 0 + 38 Reorder the terms: -38 + 38 + 0.6x + x2 = 0 + 38 Combine like terms: -38 + 38 = 0 0 + 0.6x + x2 = 0 + 38 0.6x + x2 = 0 + 38 Combine like terms: 0 + 38 = 38 0.6x + x2 = 38 The x term is 0.6x. Take half its coefficient (0.3). Square it (0.09) and add it to both sides. Add '0.09' to each side of the equation. 0.6x + 0.09 + x2 = 38 + 0.09 Reorder the terms: 0.09 + 0.6x + x2 = 38 + 0.09 Combine like terms: 38 + 0.09 = 38.09 0.09 + 0.6x + x2 = 38.09 Factor a perfect square on the left side: (x + 0.3)(x + 0.3) = 38.09 Calculate the square root of the right side: 6.17170965 Break this problem into two subproblems by setting (x + 0.3) equal to 6.17170965 and -6.17170965.Subproblem 1
x + 0.3 = 6.17170965 Simplifying x + 0.3 = 6.17170965 Reorder the terms: 0.3 + x = 6.17170965 Solving 0.3 + x = 6.17170965 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3' to each side of the equation. 0.3 + -0.3 + x = 6.17170965 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + x = 6.17170965 + -0.3 x = 6.17170965 + -0.3 Combine like terms: 6.17170965 + -0.3 = 5.87170965 x = 5.87170965 Simplifying x = 5.87170965Subproblem 2
x + 0.3 = -6.17170965 Simplifying x + 0.3 = -6.17170965 Reorder the terms: 0.3 + x = -6.17170965 Solving 0.3 + x = -6.17170965 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3' to each side of the equation. 0.3 + -0.3 + x = -6.17170965 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + x = -6.17170965 + -0.3 x = -6.17170965 + -0.3 Combine like terms: -6.17170965 + -0.3 = -6.47170965 x = -6.47170965 Simplifying x = -6.47170965Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.87170965, -6.47170965}
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