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Simplifying -1x2 + 10x = -28 Reorder the terms: 10x + -1x2 = -28 Solving 10x + -1x2 = -28 Solving for variable 'x'. Reorder the terms: 28 + 10x + -1x2 = -28 + 28 Combine like terms: -28 + 28 = 0 28 + 10x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -28 + -10x + x2 = 0 Move the constant term to the right: Add '28' to each side of the equation. -28 + -10x + 28 + x2 = 0 + 28 Reorder the terms: -28 + 28 + -10x + x2 = 0 + 28 Combine like terms: -28 + 28 = 0 0 + -10x + x2 = 0 + 28 -10x + x2 = 0 + 28 Combine like terms: 0 + 28 = 28 -10x + x2 = 28 The x term is -10x. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10x + 25 + x2 = 28 + 25 Reorder the terms: 25 + -10x + x2 = 28 + 25 Combine like terms: 28 + 25 = 53 25 + -10x + x2 = 53 Factor a perfect square on the left side: (x + -5)(x + -5) = 53 Calculate the square root of the right side: 7.280109889 Break this problem into two subproblems by setting (x + -5) equal to 7.280109889 and -7.280109889.Subproblem 1
x + -5 = 7.280109889 Simplifying x + -5 = 7.280109889 Reorder the terms: -5 + x = 7.280109889 Solving -5 + x = 7.280109889 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = 7.280109889 + 5 Combine like terms: -5 + 5 = 0 0 + x = 7.280109889 + 5 x = 7.280109889 + 5 Combine like terms: 7.280109889 + 5 = 12.280109889 x = 12.280109889 Simplifying x = 12.280109889Subproblem 2
x + -5 = -7.280109889 Simplifying x + -5 = -7.280109889 Reorder the terms: -5 + x = -7.280109889 Solving -5 + x = -7.280109889 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = -7.280109889 + 5 Combine like terms: -5 + 5 = 0 0 + x = -7.280109889 + 5 x = -7.280109889 + 5 Combine like terms: -7.280109889 + 5 = -2.280109889 x = -2.280109889 Simplifying x = -2.280109889Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.280109889, -2.280109889}
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