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Simplifying 10x2 + -31x + -12 = 0 Reorder the terms: -12 + -31x + 10x2 = 0 Solving -12 + -31x + 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'. -1.2 + -3.1x + x2 = 0 Move the constant term to the right: Add '1.2' to each side of the equation. -1.2 + -3.1x + 1.2 + x2 = 0 + 1.2 Reorder the terms: -1.2 + 1.2 + -3.1x + x2 = 0 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + -3.1x + x2 = 0 + 1.2 -3.1x + x2 = 0 + 1.2 Combine like terms: 0 + 1.2 = 1.2 -3.1x + x2 = 1.2 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 + 2.4025 Reorder the terms: 2.4025 + -3.1x + x2 = 1.2 + 2.4025 Combine like terms: 1.2 + 2.4025 = 3.6025 2.4025 + -3.1x + x2 = 3.6025 Factor a perfect square on the left side: (x + -1.55)(x + -1.55) = 3.6025 Calculate the square root of the right side: 1.89802529 Break this problem into two subproblems by setting (x + -1.55) equal to 1.89802529 and -1.89802529.Subproblem 1
x + -1.55 = 1.89802529 Simplifying x + -1.55 = 1.89802529 Reorder the terms: -1.55 + x = 1.89802529 Solving -1.55 + x = 1.89802529 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 = 1.89802529 + 1.55 Combine like terms: -1.55 + 1.55 = 0.00 0.00 + x = 1.89802529 + 1.55 x = 1.89802529 + 1.55 Combine like terms: 1.89802529 + 1.55 = 3.44802529 x = 3.44802529 Simplifying x = 3.44802529Subproblem 2
x + -1.55 = -1.89802529 Simplifying x + -1.55 = -1.89802529 Reorder the terms: -1.55 + x = -1.89802529 Solving -1.55 + x = -1.89802529 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 = -1.89802529 + 1.55 Combine like terms: -1.55 + 1.55 = 0.00 0.00 + x = -1.89802529 + 1.55 x = -1.89802529 + 1.55 Combine like terms: -1.89802529 + 1.55 = -0.34802529 x = -0.34802529 Simplifying x = -0.34802529Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.44802529, -0.34802529}
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