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Simplifying 7x(5x + 2) = 20 Reorder the terms: 7x(2 + 5x) = 20 (2 * 7x + 5x * 7x) = 20 (14x + 35x2) = 20 Solving 14x + 35x2 = 20 Solving for variable 'x'. Reorder the terms: -20 + 14x + 35x2 = 20 + -20 Combine like terms: 20 + -20 = 0 -20 + 14x + 35x2 = 0 Begin completing the square. Divide all terms by 35 the coefficient of the squared term: Divide each side by '35'. -0.5714285714 + 0.4x + x2 = 0 Move the constant term to the right: Add '0.5714285714' to each side of the equation. -0.5714285714 + 0.4x + 0.5714285714 + x2 = 0 + 0.5714285714 Reorder the terms: -0.5714285714 + 0.5714285714 + 0.4x + x2 = 0 + 0.5714285714 Combine like terms: -0.5714285714 + 0.5714285714 = 0.0000000000 0.0000000000 + 0.4x + x2 = 0 + 0.5714285714 0.4x + x2 = 0 + 0.5714285714 Combine like terms: 0 + 0.5714285714 = 0.5714285714 0.4x + x2 = 0.5714285714 The x term is 0.4x. Take half its coefficient (0.2). Square it (0.04) and add it to both sides. Add '0.04' to each side of the equation. 0.4x + 0.04 + x2 = 0.5714285714 + 0.04 Reorder the terms: 0.04 + 0.4x + x2 = 0.5714285714 + 0.04 Combine like terms: 0.5714285714 + 0.04 = 0.6114285714 0.04 + 0.4x + x2 = 0.6114285714 Factor a perfect square on the left side: (x + 0.2)(x + 0.2) = 0.6114285714 Calculate the square root of the right side: 0.781938982 Break this problem into two subproblems by setting (x + 0.2) equal to 0.781938982 and -0.781938982.Subproblem 1
x + 0.2 = 0.781938982 Simplifying x + 0.2 = 0.781938982 Reorder the terms: 0.2 + x = 0.781938982 Solving 0.2 + x = 0.781938982 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2' to each side of the equation. 0.2 + -0.2 + x = 0.781938982 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + x = 0.781938982 + -0.2 x = 0.781938982 + -0.2 Combine like terms: 0.781938982 + -0.2 = 0.581938982 x = 0.581938982 Simplifying x = 0.581938982Subproblem 2
x + 0.2 = -0.781938982 Simplifying x + 0.2 = -0.781938982 Reorder the terms: 0.2 + x = -0.781938982 Solving 0.2 + x = -0.781938982 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2' to each side of the equation. 0.2 + -0.2 + x = -0.781938982 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + x = -0.781938982 + -0.2 x = -0.781938982 + -0.2 Combine like terms: -0.781938982 + -0.2 = -0.981938982 x = -0.981938982 Simplifying x = -0.981938982Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.581938982, -0.981938982}
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