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Simplifying 10x2 + 49x + -36 = 0 Reorder the terms: -36 + 49x + 10x2 = 0 Solving -36 + 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'. -3.6 + 4.9x + x2 = 0 Move the constant term to the right: Add '3.6' to each side of the equation. -3.6 + 4.9x + 3.6 + x2 = 0 + 3.6 Reorder the terms: -3.6 + 3.6 + 4.9x + x2 = 0 + 3.6 Combine like terms: -3.6 + 3.6 = 0.0 0.0 + 4.9x + x2 = 0 + 3.6 4.9x + x2 = 0 + 3.6 Combine like terms: 0 + 3.6 = 3.6 4.9x + x2 = 3.6 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 = 3.6 + 6.0025 Reorder the terms: 6.0025 + 4.9x + x2 = 3.6 + 6.0025 Combine like terms: 3.6 + 6.0025 = 9.6025 6.0025 + 4.9x + x2 = 9.6025 Factor a perfect square on the left side: (x + 2.45)(x + 2.45) = 9.6025 Calculate the square root of the right side: 3.098790086 Break this problem into two subproblems by setting (x + 2.45) equal to 3.098790086 and -3.098790086.Subproblem 1
x + 2.45 = 3.098790086 Simplifying x + 2.45 = 3.098790086 Reorder the terms: 2.45 + x = 3.098790086 Solving 2.45 + x = 3.098790086 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 = 3.098790086 + -2.45 Combine like terms: 2.45 + -2.45 = 0.00 0.00 + x = 3.098790086 + -2.45 x = 3.098790086 + -2.45 Combine like terms: 3.098790086 + -2.45 = 0.648790086 x = 0.648790086 Simplifying x = 0.648790086Subproblem 2
x + 2.45 = -3.098790086 Simplifying x + 2.45 = -3.098790086 Reorder the terms: 2.45 + x = -3.098790086 Solving 2.45 + x = -3.098790086 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 = -3.098790086 + -2.45 Combine like terms: 2.45 + -2.45 = 0.00 0.00 + x = -3.098790086 + -2.45 x = -3.098790086 + -2.45 Combine like terms: -3.098790086 + -2.45 = -5.548790086 x = -5.548790086 Simplifying x = -5.548790086Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.648790086, -5.548790086}
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