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Simplifying 2x2 + 15x + -14 = 0 Reorder the terms: -14 + 15x + 2x2 = 0 Solving -14 + 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'. -7 + 7.5x + x2 = 0 Move the constant term to the right: Add '7' to each side of the equation. -7 + 7.5x + 7 + x2 = 0 + 7 Reorder the terms: -7 + 7 + 7.5x + x2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + 7.5x + x2 = 0 + 7 7.5x + x2 = 0 + 7 Combine like terms: 0 + 7 = 7 7.5x + x2 = 7 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 = 7 + 14.0625 Reorder the terms: 14.0625 + 7.5x + x2 = 7 + 14.0625 Combine like terms: 7 + 14.0625 = 21.0625 14.0625 + 7.5x + x2 = 21.0625 Factor a perfect square on the left side: (x + 3.75)(x + 3.75) = 21.0625 Calculate the square root of the right side: 4.589389938 Break this problem into two subproblems by setting (x + 3.75) equal to 4.589389938 and -4.589389938.Subproblem 1
x + 3.75 = 4.589389938 Simplifying x + 3.75 = 4.589389938 Reorder the terms: 3.75 + x = 4.589389938 Solving 3.75 + x = 4.589389938 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 = 4.589389938 + -3.75 Combine like terms: 3.75 + -3.75 = 0.00 0.00 + x = 4.589389938 + -3.75 x = 4.589389938 + -3.75 Combine like terms: 4.589389938 + -3.75 = 0.839389938 x = 0.839389938 Simplifying x = 0.839389938Subproblem 2
x + 3.75 = -4.589389938 Simplifying x + 3.75 = -4.589389938 Reorder the terms: 3.75 + x = -4.589389938 Solving 3.75 + x = -4.589389938 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 = -4.589389938 + -3.75 Combine like terms: 3.75 + -3.75 = 0.00 0.00 + x = -4.589389938 + -3.75 x = -4.589389938 + -3.75 Combine like terms: -4.589389938 + -3.75 = -8.339389938 x = -8.339389938 Simplifying x = -8.339389938Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.839389938, -8.339389938}
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