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Simplifying 99 + -1(10x + (x2) + 38) = 0 99 + -1(10x + x2 + 38) = 0 Reorder the terms: 99 + -1(38 + 10x + x2) = 0 99 + (38 * -1 + 10x * -1 + x2 * -1) = 0 99 + (-38 + -10x + -1x2) = 0 Combine like terms: 99 + -38 = 61 61 + -10x + -1x2 = 0 Solving 61 + -10x + -1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -61 + 10x + x2 = 0 Move the constant term to the right: Add '61' to each side of the equation. -61 + 10x + 61 + x2 = 0 + 61 Reorder the terms: -61 + 61 + 10x + x2 = 0 + 61 Combine like terms: -61 + 61 = 0 0 + 10x + x2 = 0 + 61 10x + x2 = 0 + 61 Combine like terms: 0 + 61 = 61 10x + x2 = 61 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 = 61 + 25 Reorder the terms: 25 + 10x + x2 = 61 + 25 Combine like terms: 61 + 25 = 86 25 + 10x + x2 = 86 Factor a perfect square on the left side: (x + 5)(x + 5) = 86 Calculate the square root of the right side: 9.273618495 Break this problem into two subproblems by setting (x + 5) equal to 9.273618495 and -9.273618495.Subproblem 1
x + 5 = 9.273618495 Simplifying x + 5 = 9.273618495 Reorder the terms: 5 + x = 9.273618495 Solving 5 + x = 9.273618495 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 = 9.273618495 + -5 Combine like terms: 5 + -5 = 0 0 + x = 9.273618495 + -5 x = 9.273618495 + -5 Combine like terms: 9.273618495 + -5 = 4.273618495 x = 4.273618495 Simplifying x = 4.273618495Subproblem 2
x + 5 = -9.273618495 Simplifying x + 5 = -9.273618495 Reorder the terms: 5 + x = -9.273618495 Solving 5 + x = -9.273618495 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 = -9.273618495 + -5 Combine like terms: 5 + -5 = 0 0 + x = -9.273618495 + -5 x = -9.273618495 + -5 Combine like terms: -9.273618495 + -5 = -14.273618495 x = -14.273618495 Simplifying x = -14.273618495Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.273618495, -14.273618495}
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