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Simplifying 30 = 0.7x2 + 0.5x Reorder the terms: 30 = 0.5x + 0.7x2 Solving 30 = 0.5x + 0.7x2 Solving for variable 'x'. Reorder the terms: 30 + -0.5x + -0.7x2 = 0.5x + -0.5x + 0.7x2 + -0.7x2 Combine like terms: 0.5x + -0.5x = 0.0 30 + -0.5x + -0.7x2 = 0.0 + 0.7x2 + -0.7x2 30 + -0.5x + -0.7x2 = 0.7x2 + -0.7x2 Combine like terms: 0.7x2 + -0.7x2 = 0.0 30 + -0.5x + -0.7x2 = 0.0 Begin completing the square. Divide all terms by -0.7 the coefficient of the squared term: Divide each side by '-0.7'. -42.85714286 + 0.7142857143x + x2 = 0 Move the constant term to the right: Add '42.85714286' to each side of the equation. -42.85714286 + 0.7142857143x + 42.85714286 + x2 = 0 + 42.85714286 Reorder the terms: -42.85714286 + 42.85714286 + 0.7142857143x + x2 = 0 + 42.85714286 Combine like terms: -42.85714286 + 42.85714286 = 0.00000000 0.00000000 + 0.7142857143x + x2 = 0 + 42.85714286 0.7142857143x + x2 = 0 + 42.85714286 Combine like terms: 0 + 42.85714286 = 42.85714286 0.7142857143x + x2 = 42.85714286 The x term is 0.7142857143x. Take half its coefficient (0.3571428572). Square it (0.1275510204) and add it to both sides. Add '0.1275510204' to each side of the equation. 0.7142857143x + 0.1275510204 + x2 = 42.85714286 + 0.1275510204 Reorder the terms: 0.1275510204 + 0.7142857143x + x2 = 42.85714286 + 0.1275510204 Combine like terms: 42.85714286 + 0.1275510204 = 42.9846938804 0.1275510204 + 0.7142857143x + x2 = 42.9846938804 Factor a perfect square on the left side: (x + 0.3571428572)(x + 0.3571428572) = 42.9846938804 Calculate the square root of the right side: 6.55627134 Break this problem into two subproblems by setting (x + 0.3571428572) equal to 6.55627134 and -6.55627134.Subproblem 1
x + 0.3571428572 = 6.55627134 Simplifying x + 0.3571428572 = 6.55627134 Reorder the terms: 0.3571428572 + x = 6.55627134 Solving 0.3571428572 + x = 6.55627134 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3571428572' to each side of the equation. 0.3571428572 + -0.3571428572 + x = 6.55627134 + -0.3571428572 Combine like terms: 0.3571428572 + -0.3571428572 = 0.0000000000 0.0000000000 + x = 6.55627134 + -0.3571428572 x = 6.55627134 + -0.3571428572 Combine like terms: 6.55627134 + -0.3571428572 = 6.1991284828 x = 6.1991284828 Simplifying x = 6.1991284828Subproblem 2
x + 0.3571428572 = -6.55627134 Simplifying x + 0.3571428572 = -6.55627134 Reorder the terms: 0.3571428572 + x = -6.55627134 Solving 0.3571428572 + x = -6.55627134 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3571428572' to each side of the equation. 0.3571428572 + -0.3571428572 + x = -6.55627134 + -0.3571428572 Combine like terms: 0.3571428572 + -0.3571428572 = 0.0000000000 0.0000000000 + x = -6.55627134 + -0.3571428572 x = -6.55627134 + -0.3571428572 Combine like terms: -6.55627134 + -0.3571428572 = -6.9134141972 x = -6.9134141972 Simplifying x = -6.9134141972Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.1991284828, -6.9134141972}
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