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Simplifying 7x2 + -3x + -64 = 0 Reorder the terms: -64 + -3x + 7x2 = 0 Solving -64 + -3x + 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'. -9.142857143 + -0.4285714286x + x2 = 0 Move the constant term to the right: Add '9.142857143' to each side of the equation. -9.142857143 + -0.4285714286x + 9.142857143 + x2 = 0 + 9.142857143 Reorder the terms: -9.142857143 + 9.142857143 + -0.4285714286x + x2 = 0 + 9.142857143 Combine like terms: -9.142857143 + 9.142857143 = 0.000000000 0.000000000 + -0.4285714286x + x2 = 0 + 9.142857143 -0.4285714286x + x2 = 0 + 9.142857143 Combine like terms: 0 + 9.142857143 = 9.142857143 -0.4285714286x + x2 = 9.142857143 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 = 9.142857143 + 0.04591836735 Reorder the terms: 0.04591836735 + -0.4285714286x + x2 = 9.142857143 + 0.04591836735 Combine like terms: 9.142857143 + 0.04591836735 = 9.18877551035 0.04591836735 + -0.4285714286x + x2 = 9.18877551035 Factor a perfect square on the left side: (x + -0.2142857143)(x + -0.2142857143) = 9.18877551035 Calculate the square root of the right side: 3.031299311 Break this problem into two subproblems by setting (x + -0.2142857143) equal to 3.031299311 and -3.031299311.Subproblem 1
x + -0.2142857143 = 3.031299311 Simplifying x + -0.2142857143 = 3.031299311 Reorder the terms: -0.2142857143 + x = 3.031299311 Solving -0.2142857143 + x = 3.031299311 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 = 3.031299311 + 0.2142857143 Combine like terms: -0.2142857143 + 0.2142857143 = 0.0000000000 0.0000000000 + x = 3.031299311 + 0.2142857143 x = 3.031299311 + 0.2142857143 Combine like terms: 3.031299311 + 0.2142857143 = 3.2455850253 x = 3.2455850253 Simplifying x = 3.2455850253Subproblem 2
x + -0.2142857143 = -3.031299311 Simplifying x + -0.2142857143 = -3.031299311 Reorder the terms: -0.2142857143 + x = -3.031299311 Solving -0.2142857143 + x = -3.031299311 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 = -3.031299311 + 0.2142857143 Combine like terms: -0.2142857143 + 0.2142857143 = 0.0000000000 0.0000000000 + x = -3.031299311 + 0.2142857143 x = -3.031299311 + 0.2142857143 Combine like terms: -3.031299311 + 0.2142857143 = -2.8170135967 x = -2.8170135967 Simplifying x = -2.8170135967Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.2455850253, -2.8170135967}
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