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Simplifying 7x(x + -5) = 5(4 + -3) Reorder the terms: 7x(-5 + x) = 5(4 + -3) (-5 * 7x + x * 7x) = 5(4 + -3) (-35x + 7x2) = 5(4 + -3) Combine like terms: 4 + -3 = 1 -35x + 7x2 = 5(1) Multiply 5 * 1 -35x + 7x2 = 5 Solving -35x + 7x2 = 5 Solving for variable 'x'. Reorder the terms: -5 + -35x + 7x2 = 5 + -5 Combine like terms: 5 + -5 = 0 -5 + -35x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -0.7142857143 + -5x + x2 = 0 Move the constant term to the right: Add '0.7142857143' to each side of the equation. -0.7142857143 + -5x + 0.7142857143 + x2 = 0 + 0.7142857143 Reorder the terms: -0.7142857143 + 0.7142857143 + -5x + x2 = 0 + 0.7142857143 Combine like terms: -0.7142857143 + 0.7142857143 = 0.0000000000 0.0000000000 + -5x + x2 = 0 + 0.7142857143 -5x + x2 = 0 + 0.7142857143 Combine like terms: 0 + 0.7142857143 = 0.7142857143 -5x + x2 = 0.7142857143 The x term is -5x. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5x + 6.25 + x2 = 0.7142857143 + 6.25 Reorder the terms: 6.25 + -5x + x2 = 0.7142857143 + 6.25 Combine like terms: 0.7142857143 + 6.25 = 6.9642857143 6.25 + -5x + x2 = 6.9642857143 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 6.9642857143 Calculate the square root of the right side: 2.638993315 Break this problem into two subproblems by setting (x + -2.5) equal to 2.638993315 and -2.638993315.Subproblem 1
x + -2.5 = 2.638993315 Simplifying x + -2.5 = 2.638993315 Reorder the terms: -2.5 + x = 2.638993315 Solving -2.5 + x = 2.638993315 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = 2.638993315 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 2.638993315 + 2.5 x = 2.638993315 + 2.5 Combine like terms: 2.638993315 + 2.5 = 5.138993315 x = 5.138993315 Simplifying x = 5.138993315Subproblem 2
x + -2.5 = -2.638993315 Simplifying x + -2.5 = -2.638993315 Reorder the terms: -2.5 + x = -2.638993315 Solving -2.5 + x = -2.638993315 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = -2.638993315 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -2.638993315 + 2.5 x = -2.638993315 + 2.5 Combine like terms: -2.638993315 + 2.5 = -0.138993315 x = -0.138993315 Simplifying x = -0.138993315Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.138993315, -0.138993315}
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