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Simplifying 5x2 + -29x + 15 = 0 Reorder the terms: 15 + -29x + 5x2 = 0 Solving 15 + -29x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 3 + -5.8x + x2 = 0 Move the constant term to the right: Add '-3' to each side of the equation. 3 + -5.8x + -3 + x2 = 0 + -3 Reorder the terms: 3 + -3 + -5.8x + x2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -5.8x + x2 = 0 + -3 -5.8x + x2 = 0 + -3 Combine like terms: 0 + -3 = -3 -5.8x + x2 = -3 The x term is -5.8x. Take half its coefficient (-2.9). Square it (8.41) and add it to both sides. Add '8.41' to each side of the equation. -5.8x + 8.41 + x2 = -3 + 8.41 Reorder the terms: 8.41 + -5.8x + x2 = -3 + 8.41 Combine like terms: -3 + 8.41 = 5.41 8.41 + -5.8x + x2 = 5.41 Factor a perfect square on the left side: (x + -2.9)(x + -2.9) = 5.41 Calculate the square root of the right side: 2.32594067 Break this problem into two subproblems by setting (x + -2.9) equal to 2.32594067 and -2.32594067.Subproblem 1
x + -2.9 = 2.32594067 Simplifying x + -2.9 = 2.32594067 Reorder the terms: -2.9 + x = 2.32594067 Solving -2.9 + x = 2.32594067 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.9' to each side of the equation. -2.9 + 2.9 + x = 2.32594067 + 2.9 Combine like terms: -2.9 + 2.9 = 0.0 0.0 + x = 2.32594067 + 2.9 x = 2.32594067 + 2.9 Combine like terms: 2.32594067 + 2.9 = 5.22594067 x = 5.22594067 Simplifying x = 5.22594067Subproblem 2
x + -2.9 = -2.32594067 Simplifying x + -2.9 = -2.32594067 Reorder the terms: -2.9 + x = -2.32594067 Solving -2.9 + x = -2.32594067 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.9' to each side of the equation. -2.9 + 2.9 + x = -2.32594067 + 2.9 Combine like terms: -2.9 + 2.9 = 0.0 0.0 + x = -2.32594067 + 2.9 x = -2.32594067 + 2.9 Combine like terms: -2.32594067 + 2.9 = 0.57405933 x = 0.57405933 Simplifying x = 0.57405933Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.22594067, 0.57405933}
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