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Simplifying 0 = x(7.9 + x) + -16 0 = (7.9 * x + x * x) + -16 0 = (7.9x + x2) + -16 Reorder the terms: 0 = -16 + 7.9x + x2 Solving 0 = -16 + 7.9x + x2 Solving for variable 'x'. Combine like terms: 0 + 16 = 16 16 + -7.9x + -1x2 = -16 + 7.9x + x2 + 16 + -7.9x + -1x2 Reorder the terms: 16 + -7.9x + -1x2 = -16 + 16 + 7.9x + -7.9x + x2 + -1x2 Combine like terms: -16 + 16 = 0 16 + -7.9x + -1x2 = 0 + 7.9x + -7.9x + x2 + -1x2 16 + -7.9x + -1x2 = 7.9x + -7.9x + x2 + -1x2 Combine like terms: 7.9x + -7.9x = 0.0 16 + -7.9x + -1x2 = 0.0 + x2 + -1x2 16 + -7.9x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 16 + -7.9x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -16 + 7.9x + x2 = 0 Move the constant term to the right: Add '16' to each side of the equation. -16 + 7.9x + 16 + x2 = 0 + 16 Reorder the terms: -16 + 16 + 7.9x + x2 = 0 + 16 Combine like terms: -16 + 16 = 0 0 + 7.9x + x2 = 0 + 16 7.9x + x2 = 0 + 16 Combine like terms: 0 + 16 = 16 7.9x + x2 = 16 The x term is 7.9x. Take half its coefficient (3.95). Square it (15.6025) and add it to both sides. Add '15.6025' to each side of the equation. 7.9x + 15.6025 + x2 = 16 + 15.6025 Reorder the terms: 15.6025 + 7.9x + x2 = 16 + 15.6025 Combine like terms: 16 + 15.6025 = 31.6025 15.6025 + 7.9x + x2 = 31.6025 Factor a perfect square on the left side: (x + 3.95)(x + 3.95) = 31.6025 Calculate the square root of the right side: 5.62161009 Break this problem into two subproblems by setting (x + 3.95) equal to 5.62161009 and -5.62161009.Subproblem 1
x + 3.95 = 5.62161009 Simplifying x + 3.95 = 5.62161009 Reorder the terms: 3.95 + x = 5.62161009 Solving 3.95 + x = 5.62161009 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.95' to each side of the equation. 3.95 + -3.95 + x = 5.62161009 + -3.95 Combine like terms: 3.95 + -3.95 = 0.00 0.00 + x = 5.62161009 + -3.95 x = 5.62161009 + -3.95 Combine like terms: 5.62161009 + -3.95 = 1.67161009 x = 1.67161009 Simplifying x = 1.67161009Subproblem 2
x + 3.95 = -5.62161009 Simplifying x + 3.95 = -5.62161009 Reorder the terms: 3.95 + x = -5.62161009 Solving 3.95 + x = -5.62161009 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.95' to each side of the equation. 3.95 + -3.95 + x = -5.62161009 + -3.95 Combine like terms: 3.95 + -3.95 = 0.00 0.00 + x = -5.62161009 + -3.95 x = -5.62161009 + -3.95 Combine like terms: -5.62161009 + -3.95 = -9.57161009 x = -9.57161009 Simplifying x = -9.57161009Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.67161009, -9.57161009}
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