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Simplifying 7x2 + -5x = 692 Reorder the terms: -5x + 7x2 = 692 Solving -5x + 7x2 = 692 Solving for variable 'x'. Reorder the terms: -692 + -5x + 7x2 = 692 + -692 Combine like terms: 692 + -692 = 0 -692 + -5x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -98.85714286 + -0.7142857143x + x2 = 0 Move the constant term to the right: Add '98.85714286' to each side of the equation. -98.85714286 + -0.7142857143x + 98.85714286 + x2 = 0 + 98.85714286 Reorder the terms: -98.85714286 + 98.85714286 + -0.7142857143x + x2 = 0 + 98.85714286 Combine like terms: -98.85714286 + 98.85714286 = 0.00000000 0.00000000 + -0.7142857143x + x2 = 0 + 98.85714286 -0.7142857143x + x2 = 0 + 98.85714286 Combine like terms: 0 + 98.85714286 = 98.85714286 -0.7142857143x + x2 = 98.85714286 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 = 98.85714286 + 0.1275510204 Reorder the terms: 0.1275510204 + -0.7142857143x + x2 = 98.85714286 + 0.1275510204 Combine like terms: 98.85714286 + 0.1275510204 = 98.9846938804 0.1275510204 + -0.7142857143x + x2 = 98.9846938804 Factor a perfect square on the left side: (x + -0.3571428572)(x + -0.3571428572) = 98.9846938804 Calculate the square root of the right side: 9.94910518 Break this problem into two subproblems by setting (x + -0.3571428572) equal to 9.94910518 and -9.94910518.Subproblem 1
x + -0.3571428572 = 9.94910518 Simplifying x + -0.3571428572 = 9.94910518 Reorder the terms: -0.3571428572 + x = 9.94910518 Solving -0.3571428572 + x = 9.94910518 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 = 9.94910518 + 0.3571428572 Combine like terms: -0.3571428572 + 0.3571428572 = 0.0000000000 0.0000000000 + x = 9.94910518 + 0.3571428572 x = 9.94910518 + 0.3571428572 Combine like terms: 9.94910518 + 0.3571428572 = 10.3062480372 x = 10.3062480372 Simplifying x = 10.3062480372Subproblem 2
x + -0.3571428572 = -9.94910518 Simplifying x + -0.3571428572 = -9.94910518 Reorder the terms: -0.3571428572 + x = -9.94910518 Solving -0.3571428572 + x = -9.94910518 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 = -9.94910518 + 0.3571428572 Combine like terms: -0.3571428572 + 0.3571428572 = 0.0000000000 0.0000000000 + x = -9.94910518 + 0.3571428572 x = -9.94910518 + 0.3571428572 Combine like terms: -9.94910518 + 0.3571428572 = -9.5919623228 x = -9.5919623228 Simplifying x = -9.5919623228Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.3062480372, -9.5919623228}
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