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Simplifying 10x2 + 31x + -30 = 0 Reorder the terms: -30 + 31x + 10x2 = 0 Solving -30 + 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'. -3 + 3.1x + x2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + 3.1x + 3 + x2 = 0 + 3 Reorder the terms: -3 + 3 + 3.1x + x2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 3.1x + x2 = 0 + 3 3.1x + x2 = 0 + 3 Combine like terms: 0 + 3 = 3 3.1x + x2 = 3 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 = 3 + 2.4025 Reorder the terms: 2.4025 + 3.1x + x2 = 3 + 2.4025 Combine like terms: 3 + 2.4025 = 5.4025 2.4025 + 3.1x + x2 = 5.4025 Factor a perfect square on the left side: (x + 1.55)(x + 1.55) = 5.4025 Calculate the square root of the right side: 2.32432786 Break this problem into two subproblems by setting (x + 1.55) equal to 2.32432786 and -2.32432786.Subproblem 1
x + 1.55 = 2.32432786 Simplifying x + 1.55 = 2.32432786 Reorder the terms: 1.55 + x = 2.32432786 Solving 1.55 + x = 2.32432786 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 = 2.32432786 + -1.55 Combine like terms: 1.55 + -1.55 = 0.00 0.00 + x = 2.32432786 + -1.55 x = 2.32432786 + -1.55 Combine like terms: 2.32432786 + -1.55 = 0.77432786 x = 0.77432786 Simplifying x = 0.77432786Subproblem 2
x + 1.55 = -2.32432786 Simplifying x + 1.55 = -2.32432786 Reorder the terms: 1.55 + x = -2.32432786 Solving 1.55 + x = -2.32432786 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 = -2.32432786 + -1.55 Combine like terms: 1.55 + -1.55 = 0.00 0.00 + x = -2.32432786 + -1.55 x = -2.32432786 + -1.55 Combine like terms: -2.32432786 + -1.55 = -3.87432786 x = -3.87432786 Simplifying x = -3.87432786Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.77432786, -3.87432786}
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