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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 = 7.0625 14.0625 + -7.5x + x2 = 7.0625 Factor a perfect square on the left side: (x + -3.75)(x + -3.75) = 7.0625 Calculate the square root of the right side: 2.657536453 Break this problem into two subproblems by setting (x + -3.75) equal to 2.657536453 and -2.657536453.Subproblem 1
x + -3.75 = 2.657536453 Simplifying x + -3.75 = 2.657536453 Reorder the terms: -3.75 + x = 2.657536453 Solving -3.75 + x = 2.657536453 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 = 2.657536453 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + x = 2.657536453 + 3.75 x = 2.657536453 + 3.75 Combine like terms: 2.657536453 + 3.75 = 6.407536453 x = 6.407536453 Simplifying x = 6.407536453Subproblem 2
x + -3.75 = -2.657536453 Simplifying x + -3.75 = -2.657536453 Reorder the terms: -3.75 + x = -2.657536453 Solving -3.75 + x = -2.657536453 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 = -2.657536453 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + x = -2.657536453 + 3.75 x = -2.657536453 + 3.75 Combine like terms: -2.657536453 + 3.75 = 1.092463547 x = 1.092463547 Simplifying x = 1.092463547Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.407536453, 1.092463547}
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