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Simplifying 0 = 7x2 + -3x + -36 Reorder the terms: 0 = -36 + -3x + 7x2 Solving 0 = -36 + -3x + 7x2 Solving for variable 'x'. Combine like terms: 0 + 36 = 36 36 + 3x + -7x2 = -36 + -3x + 7x2 + 36 + 3x + -7x2 Reorder the terms: 36 + 3x + -7x2 = -36 + 36 + -3x + 3x + 7x2 + -7x2 Combine like terms: -36 + 36 = 0 36 + 3x + -7x2 = 0 + -3x + 3x + 7x2 + -7x2 36 + 3x + -7x2 = -3x + 3x + 7x2 + -7x2 Combine like terms: -3x + 3x = 0 36 + 3x + -7x2 = 0 + 7x2 + -7x2 36 + 3x + -7x2 = 7x2 + -7x2 Combine like terms: 7x2 + -7x2 = 0 36 + 3x + -7x2 = 0 Begin completing the square. Divide all terms by -7 the coefficient of the squared term: Divide each side by '-7'. -5.142857143 + -0.4285714286x + x2 = 0 Move the constant term to the right: Add '5.142857143' to each side of the equation. -5.142857143 + -0.4285714286x + 5.142857143 + x2 = 0 + 5.142857143 Reorder the terms: -5.142857143 + 5.142857143 + -0.4285714286x + x2 = 0 + 5.142857143 Combine like terms: -5.142857143 + 5.142857143 = 0.000000000 0.000000000 + -0.4285714286x + x2 = 0 + 5.142857143 -0.4285714286x + x2 = 0 + 5.142857143 Combine like terms: 0 + 5.142857143 = 5.142857143 -0.4285714286x + x2 = 5.142857143 The x term is -0.4285714286x. Take half its coefficient (-0.2142857143). Square it (0.04591836735) and add it to both sides. Add '0.04591836735' to each side of the equation. -0.4285714286x + 0.04591836735 + x2 = 5.142857143 + 0.04591836735 Reorder the terms: 0.04591836735 + -0.4285714286x + x2 = 5.142857143 + 0.04591836735 Combine like terms: 5.142857143 + 0.04591836735 = 5.18877551035 0.04591836735 + -0.4285714286x + x2 = 5.18877551035 Factor a perfect square on the left side: (x + -0.2142857143)(x + -0.2142857143) = 5.18877551035 Calculate the square root of the right side: 2.277888388 Break this problem into two subproblems by setting (x + -0.2142857143) equal to 2.277888388 and -2.277888388.Subproblem 1
x + -0.2142857143 = 2.277888388 Simplifying x + -0.2142857143 = 2.277888388 Reorder the terms: -0.2142857143 + x = 2.277888388 Solving -0.2142857143 + x = 2.277888388 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2142857143' to each side of the equation. -0.2142857143 + 0.2142857143 + x = 2.277888388 + 0.2142857143 Combine like terms: -0.2142857143 + 0.2142857143 = 0.0000000000 0.0000000000 + x = 2.277888388 + 0.2142857143 x = 2.277888388 + 0.2142857143 Combine like terms: 2.277888388 + 0.2142857143 = 2.4921741023 x = 2.4921741023 Simplifying x = 2.4921741023Subproblem 2
x + -0.2142857143 = -2.277888388 Simplifying x + -0.2142857143 = -2.277888388 Reorder the terms: -0.2142857143 + x = -2.277888388 Solving -0.2142857143 + x = -2.277888388 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2142857143' to each side of the equation. -0.2142857143 + 0.2142857143 + x = -2.277888388 + 0.2142857143 Combine like terms: -0.2142857143 + 0.2142857143 = 0.0000000000 0.0000000000 + x = -2.277888388 + 0.2142857143 x = -2.277888388 + 0.2142857143 Combine like terms: -2.277888388 + 0.2142857143 = -2.0636026737 x = -2.0636026737 Simplifying x = -2.0636026737Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.4921741023, -2.0636026737}
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