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Simplifying 2x2 + 15x + -7.9 = 0 Reorder the terms: -7.9 + 15x + 2x2 = 0 Solving -7.9 + 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'. -3.95 + 7.5x + x2 = 0 Move the constant term to the right: Add '3.95' to each side of the equation. -3.95 + 7.5x + 3.95 + x2 = 0 + 3.95 Reorder the terms: -3.95 + 3.95 + 7.5x + x2 = 0 + 3.95 Combine like terms: -3.95 + 3.95 = 0.00 0.00 + 7.5x + x2 = 0 + 3.95 7.5x + x2 = 0 + 3.95 Combine like terms: 0 + 3.95 = 3.95 7.5x + x2 = 3.95 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 = 3.95 + 14.0625 Reorder the terms: 14.0625 + 7.5x + x2 = 3.95 + 14.0625 Combine like terms: 3.95 + 14.0625 = 18.0125 14.0625 + 7.5x + x2 = 18.0125 Factor a perfect square on the left side: (x + 3.75)(x + 3.75) = 18.0125 Calculate the square root of the right side: 4.244113571 Break this problem into two subproblems by setting (x + 3.75) equal to 4.244113571 and -4.244113571.Subproblem 1
x + 3.75 = 4.244113571 Simplifying x + 3.75 = 4.244113571 Reorder the terms: 3.75 + x = 4.244113571 Solving 3.75 + x = 4.244113571 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 = 4.244113571 + -3.75 Combine like terms: 3.75 + -3.75 = 0.00 0.00 + x = 4.244113571 + -3.75 x = 4.244113571 + -3.75 Combine like terms: 4.244113571 + -3.75 = 0.494113571 x = 0.494113571 Simplifying x = 0.494113571Subproblem 2
x + 3.75 = -4.244113571 Simplifying x + 3.75 = -4.244113571 Reorder the terms: 3.75 + x = -4.244113571 Solving 3.75 + x = -4.244113571 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 = -4.244113571 + -3.75 Combine like terms: 3.75 + -3.75 = 0.00 0.00 + x = -4.244113571 + -3.75 x = -4.244113571 + -3.75 Combine like terms: -4.244113571 + -3.75 = -7.994113571 x = -7.994113571 Simplifying x = -7.994113571Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.494113571, -7.994113571}
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