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Simplifying 2x2 + 3x + -15 = 0 Reorder the terms: -15 + 3x + 2x2 = 0 Solving -15 + 3x + 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'. -7.5 + 1.5x + x2 = 0 Move the constant term to the right: Add '7.5' to each side of the equation. -7.5 + 1.5x + 7.5 + x2 = 0 + 7.5 Reorder the terms: -7.5 + 7.5 + 1.5x + x2 = 0 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + 1.5x + x2 = 0 + 7.5 1.5x + x2 = 0 + 7.5 Combine like terms: 0 + 7.5 = 7.5 1.5x + x2 = 7.5 The x term is 1.5x. Take half its coefficient (0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. 1.5x + 0.5625 + x2 = 7.5 + 0.5625 Reorder the terms: 0.5625 + 1.5x + x2 = 7.5 + 0.5625 Combine like terms: 7.5 + 0.5625 = 8.0625 0.5625 + 1.5x + x2 = 8.0625 Factor a perfect square on the left side: (x + 0.75)(x + 0.75) = 8.0625 Calculate the square root of the right side: 2.839454173 Break this problem into two subproblems by setting (x + 0.75) equal to 2.839454173 and -2.839454173.Subproblem 1
x + 0.75 = 2.839454173 Simplifying x + 0.75 = 2.839454173 Reorder the terms: 0.75 + x = 2.839454173 Solving 0.75 + x = 2.839454173 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = 2.839454173 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = 2.839454173 + -0.75 x = 2.839454173 + -0.75 Combine like terms: 2.839454173 + -0.75 = 2.089454173 x = 2.089454173 Simplifying x = 2.089454173Subproblem 2
x + 0.75 = -2.839454173 Simplifying x + 0.75 = -2.839454173 Reorder the terms: 0.75 + x = -2.839454173 Solving 0.75 + x = -2.839454173 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = -2.839454173 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = -2.839454173 + -0.75 x = -2.839454173 + -0.75 Combine like terms: -2.839454173 + -0.75 = -3.589454173 x = -3.589454173 Simplifying x = -3.589454173Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.089454173, -3.589454173}
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