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Simplifying 7x2 + -28x + 15 = 0 Reorder the terms: 15 + -28x + 7x2 = 0 Solving 15 + -28x + 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 + -4x + x2 = 0 Move the constant term to the right: Add '-2.142857143' to each side of the equation. 2.142857143 + -4x + -2.142857143 + x2 = 0 + -2.142857143 Reorder the terms: 2.142857143 + -2.142857143 + -4x + x2 = 0 + -2.142857143 Combine like terms: 2.142857143 + -2.142857143 = 0.000000000 0.000000000 + -4x + x2 = 0 + -2.142857143 -4x + x2 = 0 + -2.142857143 Combine like terms: 0 + -2.142857143 = -2.142857143 -4x + x2 = -2.142857143 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = -2.142857143 + 4 Reorder the terms: 4 + -4x + x2 = -2.142857143 + 4 Combine like terms: -2.142857143 + 4 = 1.857142857 4 + -4x + x2 = 1.857142857 Factor a perfect square on the left side: (x + -2)(x + -2) = 1.857142857 Calculate the square root of the right side: 1.362770288 Break this problem into two subproblems by setting (x + -2) equal to 1.362770288 and -1.362770288.Subproblem 1
x + -2 = 1.362770288 Simplifying x + -2 = 1.362770288 Reorder the terms: -2 + x = 1.362770288 Solving -2 + x = 1.362770288 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 1.362770288 + 2 Combine like terms: -2 + 2 = 0 0 + x = 1.362770288 + 2 x = 1.362770288 + 2 Combine like terms: 1.362770288 + 2 = 3.362770288 x = 3.362770288 Simplifying x = 3.362770288Subproblem 2
x + -2 = -1.362770288 Simplifying x + -2 = -1.362770288 Reorder the terms: -2 + x = -1.362770288 Solving -2 + x = -1.362770288 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -1.362770288 + 2 Combine like terms: -2 + 2 = 0 0 + x = -1.362770288 + 2 x = -1.362770288 + 2 Combine like terms: -1.362770288 + 2 = 0.637229712 x = 0.637229712 Simplifying x = 0.637229712Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.362770288, 0.637229712}
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