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Simplifying 2x2 + 15x + -398 = 0 Reorder the terms: -398 + 15x + 2x2 = 0 Solving -398 + 15x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -199 + 7.5x + x2 = 0 Move the constant term to the right: Add '199' to each side of the equation. -199 + 7.5x + 199 + x2 = 0 + 199 Reorder the terms: -199 + 199 + 7.5x + x2 = 0 + 199 Combine like terms: -199 + 199 = 0 0 + 7.5x + x2 = 0 + 199 7.5x + x2 = 0 + 199 Combine like terms: 0 + 199 = 199 7.5x + x2 = 199 The x term is 7.5x. Take half its coefficient (3.75). Square it (14.0625) and add it to both sides. Add '14.0625' to each side of the equation. 7.5x + 14.0625 + x2 = 199 + 14.0625 Reorder the terms: 14.0625 + 7.5x + x2 = 199 + 14.0625 Combine like terms: 199 + 14.0625 = 213.0625 14.0625 + 7.5x + x2 = 213.0625 Factor a perfect square on the left side: (x + 3.75)(x + 3.75) = 213.0625 Calculate the square root of the right side: 14.596660577 Break this problem into two subproblems by setting (x + 3.75) equal to 14.596660577 and -14.596660577.Subproblem 1
x + 3.75 = 14.596660577 Simplifying x + 3.75 = 14.596660577 Reorder the terms: 3.75 + x = 14.596660577 Solving 3.75 + x = 14.596660577 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.75' to each side of the equation. 3.75 + -3.75 + x = 14.596660577 + -3.75 Combine like terms: 3.75 + -3.75 = 0.00 0.00 + x = 14.596660577 + -3.75 x = 14.596660577 + -3.75 Combine like terms: 14.596660577 + -3.75 = 10.846660577 x = 10.846660577 Simplifying x = 10.846660577Subproblem 2
x + 3.75 = -14.596660577 Simplifying x + 3.75 = -14.596660577 Reorder the terms: 3.75 + x = -14.596660577 Solving 3.75 + x = -14.596660577 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.75' to each side of the equation. 3.75 + -3.75 + x = -14.596660577 + -3.75 Combine like terms: 3.75 + -3.75 = 0.00 0.00 + x = -14.596660577 + -3.75 x = -14.596660577 + -3.75 Combine like terms: -14.596660577 + -3.75 = -18.346660577 x = -18.346660577 Simplifying x = -18.346660577Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.846660577, -18.346660577}
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