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Simplifying 10x2 + 23x + -22 = 0 Reorder the terms: -22 + 23x + 10x2 = 0 Solving -22 + 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'. -2.2 + 2.3x + x2 = 0 Move the constant term to the right: Add '2.2' to each side of the equation. -2.2 + 2.3x + 2.2 + x2 = 0 + 2.2 Reorder the terms: -2.2 + 2.2 + 2.3x + x2 = 0 + 2.2 Combine like terms: -2.2 + 2.2 = 0.0 0.0 + 2.3x + x2 = 0 + 2.2 2.3x + x2 = 0 + 2.2 Combine like terms: 0 + 2.2 = 2.2 2.3x + x2 = 2.2 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 = 2.2 + 1.3225 Reorder the terms: 1.3225 + 2.3x + x2 = 2.2 + 1.3225 Combine like terms: 2.2 + 1.3225 = 3.5225 1.3225 + 2.3x + x2 = 3.5225 Factor a perfect square on the left side: (x + 1.15)(x + 1.15) = 3.5225 Calculate the square root of the right side: 1.876832438 Break this problem into two subproblems by setting (x + 1.15) equal to 1.876832438 and -1.876832438.Subproblem 1
x + 1.15 = 1.876832438 Simplifying x + 1.15 = 1.876832438 Reorder the terms: 1.15 + x = 1.876832438 Solving 1.15 + x = 1.876832438 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 = 1.876832438 + -1.15 Combine like terms: 1.15 + -1.15 = 0.00 0.00 + x = 1.876832438 + -1.15 x = 1.876832438 + -1.15 Combine like terms: 1.876832438 + -1.15 = 0.726832438 x = 0.726832438 Simplifying x = 0.726832438Subproblem 2
x + 1.15 = -1.876832438 Simplifying x + 1.15 = -1.876832438 Reorder the terms: 1.15 + x = -1.876832438 Solving 1.15 + x = -1.876832438 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 = -1.876832438 + -1.15 Combine like terms: 1.15 + -1.15 = 0.00 0.00 + x = -1.876832438 + -1.15 x = -1.876832438 + -1.15 Combine like terms: -1.876832438 + -1.15 = -3.026832438 x = -3.026832438 Simplifying x = -3.026832438Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.726832438, -3.026832438}
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