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Simplifying 4x(5x + -7) = 9 Reorder the terms: 4x(-7 + 5x) = 9 (-7 * 4x + 5x * 4x) = 9 (-28x + 20x2) = 9 Solving -28x + 20x2 = 9 Solving for variable 'x'. Reorder the terms: -9 + -28x + 20x2 = 9 + -9 Combine like terms: 9 + -9 = 0 -9 + -28x + 20x2 = 0 Begin completing the square. Divide all terms by 20 the coefficient of the squared term: Divide each side by '20'. -0.45 + -1.4x + x2 = 0.0 Move the constant term to the right: Add '0.45' to each side of the equation. -0.45 + -1.4x + 0.45 + x2 = 0.0 + 0.45 Reorder the terms: -0.45 + 0.45 + -1.4x + x2 = 0.0 + 0.45 Combine like terms: -0.45 + 0.45 = 0.00 0.00 + -1.4x + x2 = 0.0 + 0.45 -1.4x + x2 = 0.0 + 0.45 Combine like terms: 0.0 + 0.45 = 0.45 -1.4x + x2 = 0.45 The x term is -1.4x. Take half its coefficient (-0.7). Square it (0.49) and add it to both sides. Add '0.49' to each side of the equation. -1.4x + 0.49 + x2 = 0.45 + 0.49 Reorder the terms: 0.49 + -1.4x + x2 = 0.45 + 0.49 Combine like terms: 0.45 + 0.49 = 0.94 0.49 + -1.4x + x2 = 0.94 Factor a perfect square on the left side: (x + -0.7)(x + -0.7) = 0.94 Calculate the square root of the right side: 0.969535971 Break this problem into two subproblems by setting (x + -0.7) equal to 0.969535971 and -0.969535971.Subproblem 1
x + -0.7 = 0.969535971 Simplifying x + -0.7 = 0.969535971 Reorder the terms: -0.7 + x = 0.969535971 Solving -0.7 + x = 0.969535971 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.7' to each side of the equation. -0.7 + 0.7 + x = 0.969535971 + 0.7 Combine like terms: -0.7 + 0.7 = 0.0 0.0 + x = 0.969535971 + 0.7 x = 0.969535971 + 0.7 Combine like terms: 0.969535971 + 0.7 = 1.669535971 x = 1.669535971 Simplifying x = 1.669535971Subproblem 2
x + -0.7 = -0.969535971 Simplifying x + -0.7 = -0.969535971 Reorder the terms: -0.7 + x = -0.969535971 Solving -0.7 + x = -0.969535971 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.7' to each side of the equation. -0.7 + 0.7 + x = -0.969535971 + 0.7 Combine like terms: -0.7 + 0.7 = 0.0 0.0 + x = -0.969535971 + 0.7 x = -0.969535971 + 0.7 Combine like terms: -0.969535971 + 0.7 = -0.269535971 x = -0.269535971 Simplifying x = -0.269535971Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.669535971, -0.269535971}
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