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Simplifying 10x2 + 49x + 26 = 0 Reorder the terms: 26 + 49x + 10x2 = 0 Solving 26 + 49x + 10x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. 2.6 + 4.9x + x2 = 0 Move the constant term to the right: Add '-2.6' to each side of the equation. 2.6 + 4.9x + -2.6 + x2 = 0 + -2.6 Reorder the terms: 2.6 + -2.6 + 4.9x + x2 = 0 + -2.6 Combine like terms: 2.6 + -2.6 = 0.0 0.0 + 4.9x + x2 = 0 + -2.6 4.9x + x2 = 0 + -2.6 Combine like terms: 0 + -2.6 = -2.6 4.9x + x2 = -2.6 The x term is 4.9x. Take half its coefficient (2.45). Square it (6.0025) and add it to both sides. Add '6.0025' to each side of the equation. 4.9x + 6.0025 + x2 = -2.6 + 6.0025 Reorder the terms: 6.0025 + 4.9x + x2 = -2.6 + 6.0025 Combine like terms: -2.6 + 6.0025 = 3.4025 6.0025 + 4.9x + x2 = 3.4025 Factor a perfect square on the left side: (x + 2.45)(x + 2.45) = 3.4025 Calculate the square root of the right side: 1.844586675 Break this problem into two subproblems by setting (x + 2.45) equal to 1.844586675 and -1.844586675.Subproblem 1
x + 2.45 = 1.844586675 Simplifying x + 2.45 = 1.844586675 Reorder the terms: 2.45 + x = 1.844586675 Solving 2.45 + x = 1.844586675 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.45' to each side of the equation. 2.45 + -2.45 + x = 1.844586675 + -2.45 Combine like terms: 2.45 + -2.45 = 0.00 0.00 + x = 1.844586675 + -2.45 x = 1.844586675 + -2.45 Combine like terms: 1.844586675 + -2.45 = -0.605413325 x = -0.605413325 Simplifying x = -0.605413325Subproblem 2
x + 2.45 = -1.844586675 Simplifying x + 2.45 = -1.844586675 Reorder the terms: 2.45 + x = -1.844586675 Solving 2.45 + x = -1.844586675 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.45' to each side of the equation. 2.45 + -2.45 + x = -1.844586675 + -2.45 Combine like terms: 2.45 + -2.45 = 0.00 0.00 + x = -1.844586675 + -2.45 x = -1.844586675 + -2.45 Combine like terms: -1.844586675 + -2.45 = -4.294586675 x = -4.294586675 Simplifying x = -4.294586675Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.605413325, -4.294586675}
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