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Simplifying 10x2 + -20x + -51 = 0 Reorder the terms: -51 + -20x + 10x2 = 0 Solving -51 + -20x + 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'. -5.1 + -2x + x2 = 0 Move the constant term to the right: Add '5.1' to each side of the equation. -5.1 + -2x + 5.1 + x2 = 0 + 5.1 Reorder the terms: -5.1 + 5.1 + -2x + x2 = 0 + 5.1 Combine like terms: -5.1 + 5.1 = 0.0 0.0 + -2x + x2 = 0 + 5.1 -2x + x2 = 0 + 5.1 Combine like terms: 0 + 5.1 = 5.1 -2x + x2 = 5.1 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 5.1 + 1 Reorder the terms: 1 + -2x + x2 = 5.1 + 1 Combine like terms: 5.1 + 1 = 6.1 1 + -2x + x2 = 6.1 Factor a perfect square on the left side: (x + -1)(x + -1) = 6.1 Calculate the square root of the right side: 2.469817807 Break this problem into two subproblems by setting (x + -1) equal to 2.469817807 and -2.469817807.Subproblem 1
x + -1 = 2.469817807 Simplifying x + -1 = 2.469817807 Reorder the terms: -1 + x = 2.469817807 Solving -1 + x = 2.469817807 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 2.469817807 + 1 Combine like terms: -1 + 1 = 0 0 + x = 2.469817807 + 1 x = 2.469817807 + 1 Combine like terms: 2.469817807 + 1 = 3.469817807 x = 3.469817807 Simplifying x = 3.469817807Subproblem 2
x + -1 = -2.469817807 Simplifying x + -1 = -2.469817807 Reorder the terms: -1 + x = -2.469817807 Solving -1 + x = -2.469817807 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -2.469817807 + 1 Combine like terms: -1 + 1 = 0 0 + x = -2.469817807 + 1 x = -2.469817807 + 1 Combine like terms: -2.469817807 + 1 = -1.469817807 x = -1.469817807 Simplifying x = -1.469817807Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.469817807, -1.469817807}
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