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Simplifying 10x2 + -43x + 10 = 0 Reorder the terms: 10 + -43x + 10x2 = 0 Solving 10 + -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'. 1 + -4.3x + x2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + -4.3x + -1 + x2 = 0 + -1 Reorder the terms: 1 + -1 + -4.3x + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -4.3x + x2 = 0 + -1 -4.3x + x2 = 0 + -1 Combine like terms: 0 + -1 = -1 -4.3x + x2 = -1 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 = -1 + 4.6225 Reorder the terms: 4.6225 + -4.3x + x2 = -1 + 4.6225 Combine like terms: -1 + 4.6225 = 3.6225 4.6225 + -4.3x + x2 = 3.6225 Factor a perfect square on the left side: (x + -2.15)(x + -2.15) = 3.6225 Calculate the square root of the right side: 1.903286631 Break this problem into two subproblems by setting (x + -2.15) equal to 1.903286631 and -1.903286631.Subproblem 1
x + -2.15 = 1.903286631 Simplifying x + -2.15 = 1.903286631 Reorder the terms: -2.15 + x = 1.903286631 Solving -2.15 + x = 1.903286631 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 = 1.903286631 + 2.15 Combine like terms: -2.15 + 2.15 = 0.00 0.00 + x = 1.903286631 + 2.15 x = 1.903286631 + 2.15 Combine like terms: 1.903286631 + 2.15 = 4.053286631 x = 4.053286631 Simplifying x = 4.053286631Subproblem 2
x + -2.15 = -1.903286631 Simplifying x + -2.15 = -1.903286631 Reorder the terms: -2.15 + x = -1.903286631 Solving -2.15 + x = -1.903286631 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 = -1.903286631 + 2.15 Combine like terms: -2.15 + 2.15 = 0.00 0.00 + x = -1.903286631 + 2.15 x = -1.903286631 + 2.15 Combine like terms: -1.903286631 + 2.15 = 0.246713369 x = 0.246713369 Simplifying x = 0.246713369Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.053286631, 0.246713369}
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