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Simplifying x2 + 6x2 + -5x + -30 = 0 Reorder the terms: -30 + -5x + x2 + 6x2 = 0 Combine like terms: x2 + 6x2 = 7x2 -30 + -5x + 7x2 = 0 Solving -30 + -5x + 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'. -4.285714286 + -0.7142857143x + x2 = 0 Move the constant term to the right: Add '4.285714286' to each side of the equation. -4.285714286 + -0.7142857143x + 4.285714286 + x2 = 0 + 4.285714286 Reorder the terms: -4.285714286 + 4.285714286 + -0.7142857143x + x2 = 0 + 4.285714286 Combine like terms: -4.285714286 + 4.285714286 = 0.000000000 0.000000000 + -0.7142857143x + x2 = 0 + 4.285714286 -0.7142857143x + x2 = 0 + 4.285714286 Combine like terms: 0 + 4.285714286 = 4.285714286 -0.7142857143x + x2 = 4.285714286 The x term is -0.7142857143x. Take half its coefficient (-0.3571428572). Square it (0.1275510204) and add it to both sides. Add '0.1275510204' to each side of the equation. -0.7142857143x + 0.1275510204 + x2 = 4.285714286 + 0.1275510204 Reorder the terms: 0.1275510204 + -0.7142857143x + x2 = 4.285714286 + 0.1275510204 Combine like terms: 4.285714286 + 0.1275510204 = 4.4132653064 0.1275510204 + -0.7142857143x + x2 = 4.4132653064 Factor a perfect square on the left side: (x + -0.3571428572)(x + -0.3571428572) = 4.4132653064 Calculate the square root of the right side: 2.10077731 Break this problem into two subproblems by setting (x + -0.3571428572) equal to 2.10077731 and -2.10077731.Subproblem 1
x + -0.3571428572 = 2.10077731 Simplifying x + -0.3571428572 = 2.10077731 Reorder the terms: -0.3571428572 + x = 2.10077731 Solving -0.3571428572 + x = 2.10077731 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3571428572' to each side of the equation. -0.3571428572 + 0.3571428572 + x = 2.10077731 + 0.3571428572 Combine like terms: -0.3571428572 + 0.3571428572 = 0.0000000000 0.0000000000 + x = 2.10077731 + 0.3571428572 x = 2.10077731 + 0.3571428572 Combine like terms: 2.10077731 + 0.3571428572 = 2.4579201672 x = 2.4579201672 Simplifying x = 2.4579201672Subproblem 2
x + -0.3571428572 = -2.10077731 Simplifying x + -0.3571428572 = -2.10077731 Reorder the terms: -0.3571428572 + x = -2.10077731 Solving -0.3571428572 + x = -2.10077731 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3571428572' to each side of the equation. -0.3571428572 + 0.3571428572 + x = -2.10077731 + 0.3571428572 Combine like terms: -0.3571428572 + 0.3571428572 = 0.0000000000 0.0000000000 + x = -2.10077731 + 0.3571428572 x = -2.10077731 + 0.3571428572 Combine like terms: -2.10077731 + 0.3571428572 = -1.7436344528 x = -1.7436344528 Simplifying x = -1.7436344528Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.4579201672, -1.7436344528}
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