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Simplifying 10x2 + 23x + -36 = 0 Reorder the terms: -36 + 23x + 10x2 = 0 Solving -36 + 23x + 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 + 2.3x + x2 = 0 Move the constant term to the right: Add '3.6' to each side of the equation. -3.6 + 2.3x + 3.6 + x2 = 0 + 3.6 Reorder the terms: -3.6 + 3.6 + 2.3x + x2 = 0 + 3.6 Combine like terms: -3.6 + 3.6 = 0.0 0.0 + 2.3x + x2 = 0 + 3.6 2.3x + x2 = 0 + 3.6 Combine like terms: 0 + 3.6 = 3.6 2.3x + x2 = 3.6 The x term is 2.3x. Take half its coefficient (1.15). Square it (1.3225) and add it to both sides. Add '1.3225' to each side of the equation. 2.3x + 1.3225 + x2 = 3.6 + 1.3225 Reorder the terms: 1.3225 + 2.3x + x2 = 3.6 + 1.3225 Combine like terms: 3.6 + 1.3225 = 4.9225 1.3225 + 2.3x + x2 = 4.9225 Factor a perfect square on the left side: (x + 1.15)(x + 1.15) = 4.9225 Calculate the square root of the right side: 2.218670773 Break this problem into two subproblems by setting (x + 1.15) equal to 2.218670773 and -2.218670773.Subproblem 1
x + 1.15 = 2.218670773 Simplifying x + 1.15 = 2.218670773 Reorder the terms: 1.15 + x = 2.218670773 Solving 1.15 + x = 2.218670773 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.15' to each side of the equation. 1.15 + -1.15 + x = 2.218670773 + -1.15 Combine like terms: 1.15 + -1.15 = 0.00 0.00 + x = 2.218670773 + -1.15 x = 2.218670773 + -1.15 Combine like terms: 2.218670773 + -1.15 = 1.068670773 x = 1.068670773 Simplifying x = 1.068670773Subproblem 2
x + 1.15 = -2.218670773 Simplifying x + 1.15 = -2.218670773 Reorder the terms: 1.15 + x = -2.218670773 Solving 1.15 + x = -2.218670773 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.15' to each side of the equation. 1.15 + -1.15 + x = -2.218670773 + -1.15 Combine like terms: 1.15 + -1.15 = 0.00 0.00 + x = -2.218670773 + -1.15 x = -2.218670773 + -1.15 Combine like terms: -2.218670773 + -1.15 = -3.368670773 x = -3.368670773 Simplifying x = -3.368670773Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.068670773, -3.368670773}
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