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Simplifying 10x2 + -21x + 1 = 10x + -9 Reorder the terms: 1 + -21x + 10x2 = 10x + -9 Reorder the terms: 1 + -21x + 10x2 = -9 + 10x Solving 1 + -21x + 10x2 = -9 + 10x Solving for variable 'x'. Reorder the terms: 1 + 9 + -21x + -10x + 10x2 = -9 + 10x + 9 + -10x Combine like terms: 1 + 9 = 10 10 + -21x + -10x + 10x2 = -9 + 10x + 9 + -10x Combine like terms: -21x + -10x = -31x 10 + -31x + 10x2 = -9 + 10x + 9 + -10x Reorder the terms: 10 + -31x + 10x2 = -9 + 9 + 10x + -10x Combine like terms: -9 + 9 = 0 10 + -31x + 10x2 = 0 + 10x + -10x 10 + -31x + 10x2 = 10x + -10x Combine like terms: 10x + -10x = 0 10 + -31x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. 1 + -3.1x + x2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + -3.1x + -1 + x2 = 0 + -1 Reorder the terms: 1 + -1 + -3.1x + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -3.1x + x2 = 0 + -1 -3.1x + x2 = 0 + -1 Combine like terms: 0 + -1 = -1 -3.1x + x2 = -1 The x term is -3.1x. Take half its coefficient (-1.55). Square it (2.4025) and add it to both sides. Add '2.4025' to each side of the equation. -3.1x + 2.4025 + x2 = -1 + 2.4025 Reorder the terms: 2.4025 + -3.1x + x2 = -1 + 2.4025 Combine like terms: -1 + 2.4025 = 1.4025 2.4025 + -3.1x + x2 = 1.4025 Factor a perfect square on the left side: (x + -1.55)(x + -1.55) = 1.4025 Calculate the square root of the right side: 1.184271928 Break this problem into two subproblems by setting (x + -1.55) equal to 1.184271928 and -1.184271928.Subproblem 1
x + -1.55 = 1.184271928 Simplifying x + -1.55 = 1.184271928 Reorder the terms: -1.55 + x = 1.184271928 Solving -1.55 + x = 1.184271928 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.55' to each side of the equation. -1.55 + 1.55 + x = 1.184271928 + 1.55 Combine like terms: -1.55 + 1.55 = 0.00 0.00 + x = 1.184271928 + 1.55 x = 1.184271928 + 1.55 Combine like terms: 1.184271928 + 1.55 = 2.734271928 x = 2.734271928 Simplifying x = 2.734271928Subproblem 2
x + -1.55 = -1.184271928 Simplifying x + -1.55 = -1.184271928 Reorder the terms: -1.55 + x = -1.184271928 Solving -1.55 + x = -1.184271928 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.55' to each side of the equation. -1.55 + 1.55 + x = -1.184271928 + 1.55 Combine like terms: -1.55 + 1.55 = 0.00 0.00 + x = -1.184271928 + 1.55 x = -1.184271928 + 1.55 Combine like terms: -1.184271928 + 1.55 = 0.365728072 x = 0.365728072 Simplifying x = 0.365728072Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.734271928, 0.365728072}
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