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Simplifying 10x2 + 43x + -63 = 0 Reorder the terms: -63 + 43x + 10x2 = 0 Solving -63 + 43x + 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'. -6.3 + 4.3x + x2 = 0 Move the constant term to the right: Add '6.3' to each side of the equation. -6.3 + 4.3x + 6.3 + x2 = 0 + 6.3 Reorder the terms: -6.3 + 6.3 + 4.3x + x2 = 0 + 6.3 Combine like terms: -6.3 + 6.3 = 0.0 0.0 + 4.3x + x2 = 0 + 6.3 4.3x + x2 = 0 + 6.3 Combine like terms: 0 + 6.3 = 6.3 4.3x + x2 = 6.3 The x term is 4.3x. Take half its coefficient (2.15). Square it (4.6225) and add it to both sides. Add '4.6225' to each side of the equation. 4.3x + 4.6225 + x2 = 6.3 + 4.6225 Reorder the terms: 4.6225 + 4.3x + x2 = 6.3 + 4.6225 Combine like terms: 6.3 + 4.6225 = 10.9225 4.6225 + 4.3x + x2 = 10.9225 Factor a perfect square on the left side: (x + 2.15)(x + 2.15) = 10.9225 Calculate the square root of the right side: 3.304920574 Break this problem into two subproblems by setting (x + 2.15) equal to 3.304920574 and -3.304920574.Subproblem 1
x + 2.15 = 3.304920574 Simplifying x + 2.15 = 3.304920574 Reorder the terms: 2.15 + x = 3.304920574 Solving 2.15 + x = 3.304920574 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.15' to each side of the equation. 2.15 + -2.15 + x = 3.304920574 + -2.15 Combine like terms: 2.15 + -2.15 = 0.00 0.00 + x = 3.304920574 + -2.15 x = 3.304920574 + -2.15 Combine like terms: 3.304920574 + -2.15 = 1.154920574 x = 1.154920574 Simplifying x = 1.154920574Subproblem 2
x + 2.15 = -3.304920574 Simplifying x + 2.15 = -3.304920574 Reorder the terms: 2.15 + x = -3.304920574 Solving 2.15 + x = -3.304920574 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.15' to each side of the equation. 2.15 + -2.15 + x = -3.304920574 + -2.15 Combine like terms: 2.15 + -2.15 = 0.00 0.00 + x = -3.304920574 + -2.15 x = -3.304920574 + -2.15 Combine like terms: -3.304920574 + -2.15 = -5.454920574 x = -5.454920574 Simplifying x = -5.454920574Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.154920574, -5.454920574}
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