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Simplifying 5.7 = 10x + x2 Solving 5.7 = 10x + x2 Solving for variable 'x'. Reorder the terms: 5.7 + -10x + -1x2 = 10x + -10x + x2 + -1x2 Combine like terms: 10x + -10x = 0 5.7 + -10x + -1x2 = 0 + x2 + -1x2 5.7 + -10x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 5.7 + -10x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -5.7 + 10x + x2 = 0 Move the constant term to the right: Add '5.7' to each side of the equation. -5.7 + 10x + 5.7 + x2 = 0 + 5.7 Reorder the terms: -5.7 + 5.7 + 10x + x2 = 0 + 5.7 Combine like terms: -5.7 + 5.7 = 0.0 0.0 + 10x + x2 = 0 + 5.7 10x + x2 = 0 + 5.7 Combine like terms: 0 + 5.7 = 5.7 10x + x2 = 5.7 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 = 5.7 + 25 Reorder the terms: 25 + 10x + x2 = 5.7 + 25 Combine like terms: 5.7 + 25 = 30.7 25 + 10x + x2 = 30.7 Factor a perfect square on the left side: (x + 5)(x + 5) = 30.7 Calculate the square root of the right side: 5.540758071 Break this problem into two subproblems by setting (x + 5) equal to 5.540758071 and -5.540758071.Subproblem 1
x + 5 = 5.540758071 Simplifying x + 5 = 5.540758071 Reorder the terms: 5 + x = 5.540758071 Solving 5 + x = 5.540758071 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 = 5.540758071 + -5 Combine like terms: 5 + -5 = 0 0 + x = 5.540758071 + -5 x = 5.540758071 + -5 Combine like terms: 5.540758071 + -5 = 0.540758071 x = 0.540758071 Simplifying x = 0.540758071Subproblem 2
x + 5 = -5.540758071 Simplifying x + 5 = -5.540758071 Reorder the terms: 5 + x = -5.540758071 Solving 5 + x = -5.540758071 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 = -5.540758071 + -5 Combine like terms: 5 + -5 = 0 0 + x = -5.540758071 + -5 x = -5.540758071 + -5 Combine like terms: -5.540758071 + -5 = -10.540758071 x = -10.540758071 Simplifying x = -10.540758071Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.540758071, -10.540758071}
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