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Simplifying 2x2 + 15x + -3 = 0 Reorder the terms: -3 + 15x + 2x2 = 0 Solving -3 + 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'. -1.5 + 7.5x + x2 = 0 Move the constant term to the right: Add '1.5' to each side of the equation. -1.5 + 7.5x + 1.5 + x2 = 0 + 1.5 Reorder the terms: -1.5 + 1.5 + 7.5x + x2 = 0 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + 7.5x + x2 = 0 + 1.5 7.5x + x2 = 0 + 1.5 Combine like terms: 0 + 1.5 = 1.5 7.5x + x2 = 1.5 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 = 1.5 + 14.0625 Reorder the terms: 14.0625 + 7.5x + x2 = 1.5 + 14.0625 Combine like terms: 1.5 + 14.0625 = 15.5625 14.0625 + 7.5x + x2 = 15.5625 Factor a perfect square on the left side: (x + 3.75)(x + 3.75) = 15.5625 Calculate the square root of the right side: 3.94493346 Break this problem into two subproblems by setting (x + 3.75) equal to 3.94493346 and -3.94493346.Subproblem 1
x + 3.75 = 3.94493346 Simplifying x + 3.75 = 3.94493346 Reorder the terms: 3.75 + x = 3.94493346 Solving 3.75 + x = 3.94493346 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 = 3.94493346 + -3.75 Combine like terms: 3.75 + -3.75 = 0.00 0.00 + x = 3.94493346 + -3.75 x = 3.94493346 + -3.75 Combine like terms: 3.94493346 + -3.75 = 0.19493346 x = 0.19493346 Simplifying x = 0.19493346Subproblem 2
x + 3.75 = -3.94493346 Simplifying x + 3.75 = -3.94493346 Reorder the terms: 3.75 + x = -3.94493346 Solving 3.75 + x = -3.94493346 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 = -3.94493346 + -3.75 Combine like terms: 3.75 + -3.75 = 0.00 0.00 + x = -3.94493346 + -3.75 x = -3.94493346 + -3.75 Combine like terms: -3.94493346 + -3.75 = -7.69493346 x = -7.69493346 Simplifying x = -7.69493346Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.19493346, -7.69493346}
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