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Simplifying 7x2 + 7x = 3 Reorder the terms: 7x + 7x2 = 3 Solving 7x + 7x2 = 3 Solving for variable 'x'. Reorder the terms: -3 + 7x + 7x2 = 3 + -3 Combine like terms: 3 + -3 = 0 -3 + 7x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -0.4285714286 + x + x2 = 0 Move the constant term to the right: Add '0.4285714286' to each side of the equation. -0.4285714286 + x + 0.4285714286 + x2 = 0 + 0.4285714286 Reorder the terms: -0.4285714286 + 0.4285714286 + x + x2 = 0 + 0.4285714286 Combine like terms: -0.4285714286 + 0.4285714286 = 0.0000000000 0.0000000000 + x + x2 = 0 + 0.4285714286 x + x2 = 0 + 0.4285714286 Combine like terms: 0 + 0.4285714286 = 0.4285714286 x + x2 = 0.4285714286 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + x2 = 0.4285714286 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 0.4285714286 + 0.25 Combine like terms: 0.4285714286 + 0.25 = 0.6785714286 1.25 + x2 = 0.6785714286 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 0.6785714286 Calculate the square root of the right side: 0.823754471 Break this problem into two subproblems by setting (x + 0.5) equal to 0.823754471 and -0.823754471.Subproblem 1
x + 0.5 = 0.823754471 Simplifying x + 0.5 = 0.823754471 Reorder the terms: 0.5 + x = 0.823754471 Solving 0.5 + x = 0.823754471 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 0.823754471 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 0.823754471 + -0.5 x = 0.823754471 + -0.5 Combine like terms: 0.823754471 + -0.5 = 0.323754471 x = 0.323754471 Simplifying x = 0.323754471Subproblem 2
x + 0.5 = -0.823754471 Simplifying x + 0.5 = -0.823754471 Reorder the terms: 0.5 + x = -0.823754471 Solving 0.5 + x = -0.823754471 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -0.823754471 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -0.823754471 + -0.5 x = -0.823754471 + -0.5 Combine like terms: -0.823754471 + -0.5 = -1.323754471 x = -1.323754471 Simplifying x = -1.323754471Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.323754471, -1.323754471}
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