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Simplifying -7x2 + 35x + -15 = 0 Reorder the terms: -15 + 35x + -7x2 = 0 Solving -15 + 35x + -7x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -7 the coefficient of the squared term: Divide each side by '-7'. 2.142857143 + -5x + x2 = 0 Move the constant term to the right: Add '-2.142857143' to each side of the equation. 2.142857143 + -5x + -2.142857143 + x2 = 0 + -2.142857143 Reorder the terms: 2.142857143 + -2.142857143 + -5x + x2 = 0 + -2.142857143 Combine like terms: 2.142857143 + -2.142857143 = 0.000000000 0.000000000 + -5x + x2 = 0 + -2.142857143 -5x + x2 = 0 + -2.142857143 Combine like terms: 0 + -2.142857143 = -2.142857143 -5x + x2 = -2.142857143 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 = -2.142857143 + 6.25 Reorder the terms: 6.25 + -5x + x2 = -2.142857143 + 6.25 Combine like terms: -2.142857143 + 6.25 = 4.107142857 6.25 + -5x + x2 = 4.107142857 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 4.107142857 Calculate the square root of the right side: 2.026608708 Break this problem into two subproblems by setting (x + -2.5) equal to 2.026608708 and -2.026608708.Subproblem 1
x + -2.5 = 2.026608708 Simplifying x + -2.5 = 2.026608708 Reorder the terms: -2.5 + x = 2.026608708 Solving -2.5 + x = 2.026608708 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 = 2.026608708 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 2.026608708 + 2.5 x = 2.026608708 + 2.5 Combine like terms: 2.026608708 + 2.5 = 4.526608708 x = 4.526608708 Simplifying x = 4.526608708Subproblem 2
x + -2.5 = -2.026608708 Simplifying x + -2.5 = -2.026608708 Reorder the terms: -2.5 + x = -2.026608708 Solving -2.5 + x = -2.026608708 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 = -2.026608708 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -2.026608708 + 2.5 x = -2.026608708 + 2.5 Combine like terms: -2.026608708 + 2.5 = 0.473391292 x = 0.473391292 Simplifying x = 0.473391292Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.526608708, 0.473391292}
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