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Simplifying 3x2 + -1x2 + 15x + -5 = 0 Reorder the terms: -5 + 15x + 3x2 + -1x2 = 0 Combine like terms: 3x2 + -1x2 = 2x2 -5 + 15x + 2x2 = 0 Solving -5 + 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'. -2.5 + 7.5x + x2 = 0 Move the constant term to the right: Add '2.5' to each side of the equation. -2.5 + 7.5x + 2.5 + x2 = 0 + 2.5 Reorder the terms: -2.5 + 2.5 + 7.5x + x2 = 0 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + 7.5x + x2 = 0 + 2.5 7.5x + x2 = 0 + 2.5 Combine like terms: 0 + 2.5 = 2.5 7.5x + x2 = 2.5 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 = 2.5 + 14.0625 Reorder the terms: 14.0625 + 7.5x + x2 = 2.5 + 14.0625 Combine like terms: 2.5 + 14.0625 = 16.5625 14.0625 + 7.5x + x2 = 16.5625 Factor a perfect square on the left side: (x + 3.75)(x + 3.75) = 16.5625 Calculate the square root of the right side: 4.069705149 Break this problem into two subproblems by setting (x + 3.75) equal to 4.069705149 and -4.069705149.Subproblem 1
x + 3.75 = 4.069705149 Simplifying x + 3.75 = 4.069705149 Reorder the terms: 3.75 + x = 4.069705149 Solving 3.75 + x = 4.069705149 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 = 4.069705149 + -3.75 Combine like terms: 3.75 + -3.75 = 0.00 0.00 + x = 4.069705149 + -3.75 x = 4.069705149 + -3.75 Combine like terms: 4.069705149 + -3.75 = 0.319705149 x = 0.319705149 Simplifying x = 0.319705149Subproblem 2
x + 3.75 = -4.069705149 Simplifying x + 3.75 = -4.069705149 Reorder the terms: 3.75 + x = -4.069705149 Solving 3.75 + x = -4.069705149 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 = -4.069705149 + -3.75 Combine like terms: 3.75 + -3.75 = 0.00 0.00 + x = -4.069705149 + -3.75 x = -4.069705149 + -3.75 Combine like terms: -4.069705149 + -3.75 = -7.819705149 x = -7.819705149 Simplifying x = -7.819705149Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.319705149, -7.819705149}
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