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Simplifying 2x2 + 15x + 16 = 0 Reorder the terms: 16 + 15x + 2x2 = 0 Solving 16 + 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'. 8 + 7.5x + x2 = 0 Move the constant term to the right: Add '-8' to each side of the equation. 8 + 7.5x + -8 + x2 = 0 + -8 Reorder the terms: 8 + -8 + 7.5x + x2 = 0 + -8 Combine like terms: 8 + -8 = 0 0 + 7.5x + x2 = 0 + -8 7.5x + x2 = 0 + -8 Combine like terms: 0 + -8 = -8 7.5x + x2 = -8 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 = -8 + 14.0625 Reorder the terms: 14.0625 + 7.5x + x2 = -8 + 14.0625 Combine like terms: -8 + 14.0625 = 6.0625 14.0625 + 7.5x + x2 = 6.0625 Factor a perfect square on the left side: (x + 3.75)(x + 3.75) = 6.0625 Calculate the square root of the right side: 2.46221445 Break this problem into two subproblems by setting (x + 3.75) equal to 2.46221445 and -2.46221445.Subproblem 1
x + 3.75 = 2.46221445 Simplifying x + 3.75 = 2.46221445 Reorder the terms: 3.75 + x = 2.46221445 Solving 3.75 + x = 2.46221445 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 = 2.46221445 + -3.75 Combine like terms: 3.75 + -3.75 = 0.00 0.00 + x = 2.46221445 + -3.75 x = 2.46221445 + -3.75 Combine like terms: 2.46221445 + -3.75 = -1.28778555 x = -1.28778555 Simplifying x = -1.28778555Subproblem 2
x + 3.75 = -2.46221445 Simplifying x + 3.75 = -2.46221445 Reorder the terms: 3.75 + x = -2.46221445 Solving 3.75 + x = -2.46221445 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 = -2.46221445 + -3.75 Combine like terms: 3.75 + -3.75 = 0.00 0.00 + x = -2.46221445 + -3.75 x = -2.46221445 + -3.75 Combine like terms: -2.46221445 + -3.75 = -6.21221445 x = -6.21221445 Simplifying x = -6.21221445Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.28778555, -6.21221445}
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